ML 

3834 
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UC-NRLF 


B  M  an  2DS 


W^t  ?Bnit)ersfttp  of  Cijitaso 

Founded  by  John  D.  Rockefeller 


STUDIES  IN  MELODY 


A  Dissertation  submitted  to  the  Faculty  of  the  Graduate  School  of  Arts 

and  Literature  in  Candidacy  for  the  Degree  of  Doctor  of 

Philosophy 


DEPARTMENT  OF  PSYCHOLOGY 


By 

W.  Van  Dyke  Bingham 

Instructor  in  Educational  Psychology,  Teachers  College, 
Columbia   University 


(Published  as  Monograph  Supplement  No.  50  of  the  Psychological  Review) 

THE  REVIEW  PUBLISHING  COMPANY 

BALTIMORE,  MD. 

1910 


WAVERLY    PRESS 

WILLIAMS    4   WILKINS   COMPANY 

BALTIMORE 


PREFACE. 

In  the  first  portion  of  this  monograph  are  presented  the 
results  of  investigations  made  in  the  psychological  labora- 
tory of  the  University  of  Chicago  during  the  years  1905-07. 
The  experiments  which  form  the  basis  of  the  remainder  of  the 
work  were  carried  on  during  the  year  1907-08  in  the  Harvard 
psychological  laboratory. 

To  the  directors  of  these  two  laboratories,  Professor  James 
Rowland  Angell  and  Professor  Hugo  Miinsterberg,  the  writer 
desires  to  express  his  gratitude  for  patient  counsel  and  stimu- 
lating criticism.  He  wishes  also  to  acknowledge  his  obliga- 
tion to  the  fellow-students  of  experimental  psychology,  who, 
in  the  capacity  of  observers,  made  possible  the  prosecution  of 
these  studies. 

To  the  investigations  of  Professor  R.  H.  Stetson  in  the 
field  of  rhythm  the  writer  owes  the  method  of  attack  employed 
in  studying  the  relationships  of  muscular  movement  to  the 
melody  experience ;  and  the  outline  of  a  motor  theory  of  melody 
with  which  the  present  study  is  brought  to  a  close  is  obviously 
the  outgrowth  of  suggestions  from  Professor  Stetson's  impor- 
tant publications.  Indebtedness  to  Professor  Max  Meyer  is 
likewise  evident,  and  nowhere  more  plainly  than  in  those  pas- 
sages which  express  disagreement  with  his  views. 

My  controversy  with  Professor  Meyer  is  in  part  made 
necessary  because  of  what  seems  to  me  to  be  an  equivocal  use  of 
the  term  'tonal  relationship'  on  his  part ;  and  lest  a  similar  ambig- 
uity creep  in  to  vitiate  the  discussions  of  the  following  pages, 
I  have  taken  pains  in  each  instance  to  specify  in  which  of  its 
two  common  meanings  the  term  "relationship "  is  used.  Musi- 
cians speak  of  two  tones  as  directly  "related"  when  the  ratios 
of  their  vibration-rates  are  so  simple  that  one  tone  is  found 
among  the  first  five  partials  of  the  other,  or,  what  amounts  to 
the  same  thing,  when  the  two  tones  belong  to  a  major  triad, 
the  'chord  of  nature.'     The  "feeling  of  relationship"  is  the 


218505 


iv  PREFACE 

experience  of  coheience,  of  'belonging- togetherness,'  which 
characterizes  the  hearing  of  two  successive  tones  of  the  sort 
described.  The  question  as  to  what  pairs  of  tones  arouse  this 
feeling  of  "  relationship  "  must  of  course  be  answered  not  by  an 
arbitrary  definition  but  by  reference  to  the  facts  of  experience. 

Now  it  is  perfectly  evident  that  this  particular  kind  of  tonal 
"relationship,"  arising  out  of  certain  acoustical  properties 
of  the  sounds,  is  not  the  sole  kind  of  relationship  which  may 
bind  tones  together  in  our  experience.  Two  tones  may  come 
to  be  felt  as  related,  in  a  way,  merely  because  they  have  often 
been  heard  together.  Moreover  any  two  tones  whatsoever,  be 
their  ratios  simple  or  complex,  are  felt  to  be  related  to  each 
other  as  higher  and  lower.  Here  the  term  relationship  is  used 
in  its  ordinary  broad,  untechnical  sense. 

Whenever,  in  the  following  pages,  the  terms  "relationship" 
and  "related"  are  employed  in  the  technical  sense,  they  are 
enclosed  in  quotation  marks;  and  where  these  marks  are  not 
used,  the  reader  is  to  understand  that  the  broader,  untech- 
nical connotation  is  indicated. 

What  the  musician  designates  as  tone-color  or  timbre,  I 
have  called  by  the  usual  psychological  terms,  clang-color,  or 
briefly,  color. 


CONTENTS 
Part  I.    The  Melody  Problem  page 

§1.  The  nature  of  melody.  Three  usages  of  the  term,  corresponding  to  three 
distinct  melodic  phenomena.  A  melody  is  a  succession  of  tones  which 
are  not  only  related,  but  which  also  constitute  an  esthetic  unity,  a  whole . .         i 

§2.    An  illustration 3 

§3.     The  melody  problem:  How  can  a  series  of  discrete  tonal  stimuli  generate 

the  experience  of  melodic  unity? 4 

§4.     Elements  of  melodic  structure :  actual  duration  of  the  sounds,  pitch,  color  and 

intensity   5 

§5.     Relative  duration,  intensity  and  color 6 

§6 .  Pitch  relations ,  the  sine  qua  non :  Melodic ' '  relationship ' '  direct  and  indirect ; 
pitch  distance;  definite  and  indefinite  pitch  relations;  the  phenomenon  of 
the  falling  inflection 8 

§7.  The  phenomenon  of  melodic  trend:  certain  pairs  of  tones  heard  in  succession 
end  better  on  the  upper  tone,  others  on  the  lower.  Lipps  formulates  these 
facts  in  the '  law  of  the  powers  of  2.'     His  theoretical  assumptions 10 

§8.     Restatement  of  the  melody  problem  and  limitation  of  the  present  study  to 

effects  of  pitch 13 

Part  II:    The  Phenomena  of  Melodic  "Relationship,"  and  of  Melodic 

Trend. 

§9.  Previous  experimental  studies.  Meyer  finds  melodies  played  with  an  intona- 
tion which  admits  the  7  ratio  are  preferred  to  the  same  melodies  played  in 
the  diatonic  scale 15 

§io.    Meyer's  theory  of  melody.     Melodic  "  relationship "  observable  in  intervals 

involving  the  7  ratio.     The  'complete  scale' 17 

§11.  Dangers  arising  from  the  use  of  arithmetical  ratios  to  express" relationship." 
Any  given  feeling  of  "relationship"  is  the  property  not  of  a  single  interval 
alone,  but  of  a  whole  zone  of  intervals 21 

5i2.     First  series  of  experiments  on  the  phenomenon  of  melodic  trend,  or  finality 

in  two-tone  sequences.     Method.    Observers 23 

§13.     Discussion  of  results,     (a)  The  trend  of  the  different  intervals  compared 27 

§14.     (Jb)  The  second  tone  of  a  two-tone  group  is  judged  to  be  a  final  tone  less  often 

than  it  is  judged  to  be  lacking  in  finality    28 

§15.^    (c)     A  small  preponderance  exists  in  favor  of  descending  intervals  as  more 
"  ;i      definitely  final.    Meyer's  experiments  on  this  point.     Need  of  separating 
effects  of  the  falling  inflection  phenomenon  from  effects  due  to  more 
definite  pitch  relations 28 

§16.  {d)  When  2  is  the  end-tone,  effects  of  rising  and  falling  inflection  come 
clearly  to  view.  When  2  is  the  first  tone,  the  number  of  affirmative  judg- 
ments of  finaUty  is  nearly  the  same  for  ascending  and  for  descending 
intervals,  being  less  than  one-fourth  of  the  total  in  each  case 30 


vi  CONTENTS 

§17.     Final  summary  lends  some  support  to  the  Lipps-Meyer  law,  but  numerous    page 
exceptions  demand  explanation 32 

518.  Further  experiments  point  toward  the  'law  of  the  return,'  and  toward  the 

fact  that  tonality,  resting  on  a  harmonic  basis,  determines  melodic 
trends  even  in  tv/o-tone  sequences 33 

519.  Third  series  of  experiments:    When  a  definite  tonality  is  in  mind,  the 

trend  of  a  two-tone  sequence  is  uniformly  toward  one  of  the  tones  of 

the  tonic  chord 35 

§20.    The  nature  of  'tonality.'    A  tonality  is  an  'attitude,'  probably  motor  at 

basis 36 

i2i.    The  effects  of  habituation 39 

«  22.    Summary,  and  new  formulation  of  problem 41 

Part  III.     Effects  of  Melodic  Stimuli  upon  Muscular  Movement. 

§23.    Apparatus  for  recording  rate,  amplitude  and  form  of  tapping  movement  of 

finger    43 

§24.    Method  of  procedure 46 

§25.    Observers:  tests  of  their  musical  ability;  individual  differences  in  natural 

rate  and  form  of  tapping 48 

§26.     Results.      Records  of  tapping  without  stimulus  or  distraction 53 

§27.    Effect  of  auditory  stimuli  upon  rate  of  tapping 54 

§28.     Experiments  with  melodic  stimuli :  the  perfect  fourth.     Characteristic  vari- 
ations of  rate  of  tapping  appear,  which  are  different  for  the  ascending  and 

the  descending  fourth 57 

§29.    Hypothesis  regarding  the  significance  of  accelerations  and  retardations  of 

rate  of  tapping 59 

§30.    The  hypothesis  applied  in  detail  to  the  results  of  experiments  with  ascending 

and  descending  fourth 61 

§3 1 .    And  tested  in  the  light  of  experiments  with  the  perfect  fifth,  diminished  fifth, 

major  third  and  minor  sixth 63 

§32.    A  group  of  experiments  with  three-tone  sequences.    The  'return;'  the 

octave 69 

§33.     Effects  of  a  longer  series  of  tones  upon  the  rate  of  tapping 77 

$34.     Summary jg 

Part  IV.    Suggestions  Toward  a  Motor  Theory  of  Melody. 

§35.     Sketch  of  a  motor  theory  of  melodic  unity.     Motor  phenomena  of  mel- 
ody and  of  rhythm  compared.    Final  summary 81 


PART  I. 

THE  MELODY  PROBLEM. 

§1.  Neither  musicians  nor  psychologists  are  agreed  as  to 
the  meaning  of  the  term  melody.  Divergent  usage,  leading  to 
misunderstanding  and  dispute,  has  arisen  because  within  the 
range  of  melody  experience  there  exist  several  distinguishable 
mental  phenomena,  each  of  which  has  in  turn  been  construed 
as  the  essential  mark  of  a  melody.  Weinmann,^  following  Lipps,^ 
says  that  a  melody  is  a  unity,  a  whole,  no  mere  succession  of 
tones.  It  is,  further,  an  esthetic  unity  in  which  the  con- 
stituent tonal  elements  are  subordinated  to  a  single  dominating 
element,  the  tonic.  This  definition  operates  to  limit  the  scope 
of  his  study  to  such  melody  phenomena  as  those  exhibited  in 
modern  European  diatonic  music,  since  it  a  priori  excludes  the 
possibility  of  melodies  which  lack  tonality. 

The  doctrine  of  Lipps  and  his  followers  that  esthetic  unity 
always  involves  the  subordination  of  the  separate  elements  of  a 
manifold  to  a  single  chief  element  is  opposed  by  Meyer^.  In 
his  view,  the  statement  that  a  melody  is  a  unity  means 
merely  that  we  experience  relationship  between  the  tones. 
Indeed  Meyer  defines  melody  in  terms  of  relationship.*  To  say 
that  two  tones  are  related  and  to  say  that  they  form  a  melody  is 
the  same  thing.  Such  a  definition  avoids  a  narrow  conception 
of  melody.  The  scope  of  the  term  becomes  much  contracted, 
however,  by  the  technical  meaning  which  Meyer  attaches  to  the 
term  relationship.  The  essence  of  melody  consists,  for  Meyer, 
not  in  the  experience  of  any  kind  of  relationship  whatever 
between  the  successive  tones,  but  in  the  experience  of  a  very 

^Tritz  Weinmann:  "Zur  Struktur  der  Melodic"  Zeits.f.  Psychol.  1904,  35,  340. 

*Th.  Lipps:  "Zur  Theorie  der  Melodie,"  Zeits.  f.  Psychol.  1902,  27,  237.  See  also 
his  Psychologische  Studien,  2te  Aufl.  1905,  193  ff. 

*M.  Meyer.  "Unscientific  Methods  in  Musical  Esthetics."  Jour,  of  Phil. 
Psy.,  and  S.  M.  1904,  i,  711. 

*  Elements  of  a  Psychological  Theory  of  Melody.    Psych.  Rev,  1900,  7,  246. 


W.  VAN  DYKE  BINGHAM. 


speckildrid-HiTiited  kind  of  relationship,  namely  that  to  which 
the  technical  musical  term  "relationship"  has  come  to  be 
applied.  This  narrowing  of  the  meaning  of  the  term  operates 
to  exclude  from  the  realm  of  melody  those  songs  of  primitive 
peoples  in  which  vague  and  indefinite  pitch  intervals  appear, 
as  well  as  the  so-called  melodies  of  speech. 

Can  we  assent  to  Meyer's  contention  against  Weinmann 
that  melodic  unity  means  nothing  more  than  relationship 
between  the  parts?  The  esthetic  unity  which  characterizes 
a  melody  does  indeed  involve  experience  of  relationship  among 
the  several  tones;  but  this  is  not  all.  For  example,  it  involves 
also  the  experience  of  completeness.  If  the  feeling  of  complete- 
ness is  destroyed,  the  'unity'  is  shattered.  Not  merely  tonal 
relationship,  but  'form'  is  necessary  to  constitute  the  esthetic 
unity  of  a  melody.  Meyer's  deed  here  is  better  than  his  word : 
for  throughout  his  investigations  he  searches  for  something 
more  than  mere  "relationship"  in  his  melodies,  namely,  for  an 
organization  of  relationships,  a  combination  of  related  tones 
ordered  in  one  way  rather  than  another, — arranged,  indeed,  so 
that  they  generate  not  a  mere  consciousness  that  the  elements 
are  related,  but  a  perception  that  they  are  so  related  as  to  form 
a  complete  structure,  a  whole. 

There  are  then,  three  clearly  distinguishable  phenomena, 
each  one  of  which  has  been  put  forward  as  the  peculiar  differ- 
entia of  melody:  (a)  "relationship"  between  the  constituent 
tones;  (b)  esthetic  unity  or  wholeness,  such  as  distinguishes  a 
definite  melodic  phrase  when  contrasted  with  a  mere  fragment 
of  melody,  or  which  characterizes  even  more  clearly  a  com- 
plete melody  that  is  brought  into  comparison  with  any  portion 
of  itself;  (c)  tonality,  or  the  dominance  of  the  entire  sequence 
by  a  single  tone,  the  tonic.  Weinmann's  definition  stresses 
the  third  of  these  phenomena:  if  there  exists  a  song  of  some 
alien  people  in  which  the  preponderance  of  one  tone  over  the 
others  fails  to  appear,  such  a  song  must  be  called  by  some 
other  name  than  melody.  Meyer  at  the  opposite  extreme, 
emphasizes  only  the  phenomenon  of  "relationship."  Wher- 
ever "relationship"  between  successive  tones  is  felt,  a  melody 
exists,  even  though  the  succession  be  fragmentary  and  the 
hearer  be  left  in  suspense,  unsatisfied. 


STUDIES  IN  MELODY.  3 

For  the  purpose  of  the  present  exposition,  it  has  seemed  best 
in  defining  what  shall  be  meant  by  a  melody,  to  place  emphasis 
upon  the  second  of  these  three  phenomena, — upon  the  esthetic 
unity,  the  wholeness,  which  characterizes  the  completed  expe- 
rience. This  usage  of  the  term  is  adopted  with  full  realization 
that  it  is  not  wholly  unobjectionable.  After  such  a  definition, 
how  shall  one  speak  of  Wagner 's  '  endless  melodies  ? '  By  what 
name  shall  one  describe  the  effect  when  in  a  Brahms  chorus, 
one  of  the  middle  voices  for  a  few  brief  measures  stands 
prominently  forth  only  to  be  lost  to  the  ear  again  in  a  maze 
of  counterpoint?  Is  not  this  tonal  group  without  distinguish- 
able beginning  or  end  a  most  delightful  melody?  It  would 
certainly  be  called  a  melody  if,  with  Meyer,  we  had  chosen  to 
make  "relationship"  the  sole  essential;  but  in  the  terminology 
we  have  chosen,  it  must  be  called  a  melodic  fragment,  and  not, 
strictly,  a  melody. 

The  matter  of  prime  importance  is,  of  course,  to  realize 
that  by  whatever  names  they  may  be  called,  we  are  confronted 
with  three  different  phenomena — "relationship,"  phrase-  or 
period-unity,  tonality — which,  no  matter  how  intimately  they 
may  prove  to  be  bound  up  together,  are  nevertheless  in  intro- 
spection clearly  distinguishable,  and  must  not  be  confused. 

§2.  At  the  risk  of  incurring  the  charge  of  prolixity  from 
readers  who  are  most  at  home  in  this  field,  I  shall  venture  to 
develop  somewhat  more  fully  what  I  mean  by  a  melody,  before 
attempting  to  formulate  explicitly  the  melody  problem. 

Let  the  reader  ask  himself  in  what  way  his  experience  of  a 
melody  differs  from  his  experience  of  a  mere  succession  of 
musical  sounds  of  varying  pitch.  Possibly  he  will  reply  that 
the  group  of  sounds  that  he  calls  a  melody  is  more  pleasing. 
But  this  agreeableness  he  will  admit  is  not  the  essential  char- 
acter. One  may,  for  example,  upon  hearing  a  flageolet  of  ob- 
noxious tone  quality  find  the  whole  experience  disagreeable 
and.  yet  recognize  that  what  he  is  hearing  is  a  melody ;  or  on 
the  other  hand  one  may  take  delight  in  a  perfectly  random 
series  of  sounds  drawn  from  a  beautifully  voiced  instrument. 
Something  other  than  the  pleasurable  affective  aspect  of  the 


4  W.  VAN  DYKE  BINGHAM. 

total  experience  must  be  present  to  differentiate  the  melody 
from  the  non-melodic  succession  of  pitches. 

Upon  further  comparison  of  the  two  kinds  of  experience  the 
observer  will  notice  that  the  sounds  of  the  melody  seem  to  be- 
long together,  to  cohere,  and  to  stand  in  such  a  relationship 
each  to  the  others  that  the  entire  series  is  felt  to  be  a  unity. 
The  tones  of  the  non-melody,  by  contrast,  are  felt  to  be  unre- 
lated :  they  do  not '  hang  together'  as  it  were.  Or,  even  if  one 
discovers  that  some  of  the  tones  of  the  non-melodic  group 
exhibit  a  close  connection  with  some  of  the  others,  the  group 
as  a  whole  is  not  a  unity :  it  is  felt  to  lack  consistency  or  internal 
coherence,  or  continuity,  or  completeness. 

An  example  will  make  more  obvious  this  contrast  between  the 
melody  and  the  non-melody.  I  played  to  a  group  of  moderately 
musical  observers  the  following  simple  succession  of  musical 
sounds :  c'  e'  g'  e'  f  d'  c' .  The  tempo  was  slow,  the  duration  of 
the  tones  uniform.  I  then  played  a  second  series  beginning  on  the 
same  tone  and  ending  on  the  same  tone,  and  employing  the  same 
five  degrees  of  pitch  as  the  first  but  in  a  different  order:  c'  f  d!  g' 
e'  f  c' .  The  hearers  reported  that  in  the  first  group  the  sounds 
seemed  to  follow  each  other  naturally,  coherently,  and  in  a  way, 
inevitably,  and  with  the  last  sound  the  series  seemed  to  come  to  a 
definite  close.  Each  element  articulated  with  the  others  and  the 
group  as  a  whole  was  felt  to  be  a  unity.  In  other  words,  it  was 
judged  to  be  a  melody.  But  with  the  second  series  of  tones  the 
hearers  failed  to  discover  this  naturalness  or  inevitableness 
about  the  order  of  the  sounds.  The  pitch,  they  said,  wandered 
rather  incoherently  and  disconnectedly  here  and  there.  More- 
over when  the  last  sound  was  heard  it  failed  to  bring  the  feeling 
of  completeness,  of  finality,  which  characterized  the  close  of  the 
former  series.  This  second  succession  of  tones  was  judged  by 
these  observers  to  be  no  melody. 

§3.  Our  definition  of  a  melody  places  stress  upon  the  experi- 
ence of  unity;  but  it  does  not  prejudge  the  question  as  to 
whether  this  necessitates  the  subordination  of  all  the  elements 
to  one  dominating  'monarch  element.'  Neither  does  it  imply 
that  the  experience  of  definite  "melodic  relationships"  (in  the 
technical  sense  of  the  term)  is  the  sine  qua  non.    A  melody  we 


STUDIES  IN  MELODY.  5 

shall  define  as  a  succession  of  musical  sounds  which  is  felt  to  con- 
stitute an  esthetic  unity,  a  unity  toward  the  establishment  of 
which  the  pitch  relations  of  the  successive  tones  contribute.^ 

The  melody  problem,  then,  is  the  problem  of  explaining  how  a 
series  of  discrete  tonal  stimuli  can  arouse  this  feeling  of  unity. 

As  a  matter  of  fact  any  actual  melody  such  as  a  gamin  whistles 
on  the  street  or  a  Pawnee  Indian  sings  to  the  dawn,  gains  its 
unity,  its  coherence,  its  wholeness,  through  the  combined  oper- 
ation of  many  factors.  The  factors  of  intensity  and  duration, 
for  example,  are  coordinate  with  pitch  in  the  determination  of 
the  total  psychosis:  tempo,  rhythm,  dynamic  structure  share 
in  determining  what  the  melody  shall  be.  A  brief  analysis  of 
these  factors  will  bring  into  prominence  the  particular  phases 
of  the  melody  problem  with  which  these  studies  are  concerned. 

§4  It  is  to  be  remembered  that  musical  sounds  can  vary 
one  from  another  in  only  four  ways:  in  duration,  intensity, 
clang-color  (i.  e.,  tone-quality  or  timbre)  and  pitch.  But  each  of 
these  four  aspects  or  attributes  of  the  constituent  tones  affects 
in  a  two-fold  manner  the  nature  of  the  melody.  The  total  effect 
is  what  it  is,  partly  because  of  the  relative  duration,  intensity, 
pitch  and  color  of  the  separate  sounds  employed,  and  partly 
because  of  the  actual  pitch,  intensity,  duration  and  color.  The 
'actual  duration'  factor,  for  instance,  is  the  tempo.  The  rela- 
tive duration  of  all  the  sounds  remaining  constant,  the  nature 
of  the  melody  may  be  entirely  altered  merely  by  changing  the 
speed,  i.  e.,  the  actual  duration  of  the  sounds.  A  familiar  melody 
played  in  an  unusual  tempo  may  be  hardly  recognizable,  and 
if  the  change  of  time  is  carried  beyond  certain  limits  in  either 
direction  the  melody  is  utterly  destroyed, — it  becomes  a  con- 
fusion of  noises  or  a  broken  succession  of  sounds  without  signifi- 
cance or  interest. 

Similarly,  the  actual  or  '  absolute '  pitch  of  a  melody  enters  in 
to  make  it  what  it  is.  The  low  rumbling  melody  with  which 
Grieg  begins  the  "Dance  of  the  Trolls"  in  the  first  Peer  Gynt 
suite  is  almost  a  totally  different  thing  when  played  in  the  twice- 
accented  octave,  instead  of  three  octaves  lower. 

1  Here  and  throughout  the  paper,  whenever  the  technical  connotation  of  the  term 
"relationship"  is  indicated,  the  word  is  enclosed  in  double  quotation  marks. 


5  W.  VAN  DYKE  BINGHAM. 

The  difference  which  the  actual  clang-color  makes  is  of  course 
at  the  basis  of  artistic  orchestration  of  melodies  ^and  of  organ- 
registration.  When  a  theme  given  out  by  the  oboe  is  repeated 
by  the  violins  we  say  it  is  the  same  melody,  and  yet  it  is  not 
wholly  the  same. 

Fourthly,  the  dynamic  factor,  the  actual  loudness  or  softness 
of  the  melody  as  a  whole,  remains  to  be  mentioned  as  one  of  the 
contributors  to  the  nature  of  the  melody. 

§5.  These  four  factors  taken  in  their  actual  or  'abso  lute' 
aspects  are,  however,  of  very  secondary  significance  as  com- 
pared with  these  same  factors  operating  within  the  melody 
itself  to  contrast  and  to  bind  together  the  separate  tonal  ele- 
ments. With  reference  to  the  relative  duration,  pitch,  etc.,  of 
the  individual  tones,  it  will  be  convenient  to  treat  of  {i)  the  re- 
lation of  each  tone  to  its  immediate  associates,  and  {ii)  the 
relation  of  the  tone  to  the  whole  melody.  {Cf.  accompanying 
outline). 

ELEMENTS  OF  MELODIC  STRUCTURE  CLASSIFIED  ACCORDING  TO  THE 

FACTORS  OF 


I. 

Duration 

\ 

a)  Actual 

b)  Relative 

{,Tempo) 

i.  Measure  pattern 

Rhythmical  figuration 
ii.  Accel.,  Rit.,  etc. 

II. 

Intensity 

a)  Actual 

b)  Relative 

i.  Accent,  stress,  etc. 
ii.  Cresc. ,  decresc. ,  etc. 

III. 

Color 

a)  Actual 

b)  Relative 

(Orchestraiion;  Registration) 

i. 
ii. 

IV. 

Pitch 

a)  Actual 

b)  Relative 

(Absolute  pitch) 

i.  Interval  relationships 
ii.  Tonality  relationships 

Relations  of  duration  of  the  first  sort  are  at  the  basis  of  the 
measure-form  and   rhythmical  figures,  while  accelerando  and 


STUDIES  IN  MELODY. 


ritardando  illustrate  the  relations  to  a  more  inclusive  group. 
Rhythm  is  usually  a  result  of  the  combination  of  intensity  and 
duration  relations,  although  this  is  not  always  the  case.  Thus  a 
melody  played  on  the  organ  or  on  a  mechanical  piano  player 
lacks  variations  of  intensity  of  the  separate  tones. 

In  the  case  of  the  loudness  factor,  the  former  type  of  relation 
determines  the  effects  of  accent,  of  stress;  while  the  latter  gives 
dynamic  form  to  the  whole  group,  the  crescendo-decrescendo 
effects,  etc. 

The  relative  color  of  thf  separate  tones  has,  in  the  enumer- 
ation of  the  factors  of  melodic  structure,  usually  been  neglected. 
But  a  priori,  one  would  expect  this  attribute  of  tone-sensation, 
as  well  as  the  others,  to  be  of  significance ;  and  a  posteriori,  color 
is  found  to  be  of  vastly  greater  importance  to  melody  than  one 
might  suppose  who  had  never  given  the  matter  careful  thought. 
The  reason  why  this  factor  has  been  overlooked  is  that  it  usually 
remains  constant  throughout  the  melody.  Its  presence  as  a 
unifying  factor  first  comes  into  evidence  when  an  unwonted 
change  of  color  enters  and  makes  itself  felt  as  a  disturbing  ele- 
ment: as  when  a  singer  is  not  skillful  in  passing  from  one 
register  of  the  voice  to  another,  or  a  clarinetist  meets  a  similar 
difficulty  in  making  the  transition  from  the  lower  to  the  middle 
register  of  his  instrument.  The  changes  in  color  which  are  thus 
unwittingly  or  unavoidably  introduced  have  their  disintegrating 
effect,  be  it  never  so  slight,  upon  the  melody.  Among  violinists 
this  is  a  well  known  fact,  a  commonplace.  Even  so  slight  a 
change  of  color  as  is  involved  in  the  passage  from  one  string  to  an- 
other is  recognized  as  of  importance  in  artistic  phrasing,  and  the 
resources  of  technical  proficiency  are  sometimes  taxed  in  the  ef- 
fort to  meet  the  requirements  which  this  principle  imposes.  Such 
a  principle  raises  a  prohibition  against  careless  shifts  of  color, 
and  at  the  same  time  offers  a  positive  aid  to  artistic  phrasing, — 
it  ^rjables  the  violinist  to  give  to  a  group  of  tones  a  peculiar  unity 
of  its  own  not  otherwise  obtainable.  Surely  such  a  factor  in  the 
determination  of  melodic  form  as  clang-color, — a  factor  which  has 
a  recognized  place  in  musical  practice, — does  not  deserve  to  be 
entirely  neglected.  A  careful  experimental  study  of  the  effects 
and  of  the  possible  extent  of  alterations  of  color  within  the  mel- 
ody is  a  psychological  desideratum. 


8  W.  VAN  DYKE  BINGHAM. 

§6.  All  of  the  factors  which  have  been  discussed,  the  rela- 
tive clang-color,  loudness  and  duration  of  the  sounds,  have  been 
shown  to  contribute  to  the  structural  unity  of  a  melody.  But 
not  all  of  these  taken  together  are  sufficient  to  make  a  melody. 
The  essential  factor  is  still  lacking,  namely  the  pitch  relations. 
A  sequence  of  tones  of  the  proper  relative  loudness  and  duration 
to  constitute  a  vigorous  rhythm  would  not  be  called  a  melody  if 
the  pitch  of  the  tones  were  either  uniform  or  random. 

The  pitch,  too,  of  each  tone  bears  certain  relations  to  the 
group  of  tones  as  a  whole.  This  makes  possible  such  phenom- 
ena as  tonality,  of  which  it  will  be  necessary  to  treat  in  due 
time.  At  present  let  us  focus  attention  upon  the  relations  which 
may  exist  between  individual  tones. 

These  relations  between  tone  and  tone  are  of  several  distinct 
types.  That  type  which  has  received  fullest  treatment  at  the 
hands  of  the  musical  theorist  is  the  one  which  has  appropriated 
to  itself  as  a  technical  term  the  word  "relationship."  Two  con- 
secutive tones  were  said  by  Helmholtz^  to  be  "directly  related" 
if  they  form  a  perfectly  consonant  interval,  in  which  case  one 
of  the  clearly  perceptible  upper  partials  of  the  first  is  identical 
with  one  of  the  second;  while  to  be  "indirectly  related"  the  two 
tones  must  each  stand  in  some  such  direct  "relationship"  to  a 
common  third  tone.  This  theory  of  "relationship"  was  used 
by  him  to  account  for  the  melodic  intervals  of  the  diatonic 
scale.  To  account  for  the  appearance  of  chromatic  intervals, 
'accidentals',  in  melodies,  Helmholtz  further  recognized  a  "rela- 
tionship by  propinquity";  the  'accidental,'  he  said,  is  'related' 
to  its  neighbor  by  the  mere  fact  of  nearness.  The  fundamentally 
important  type  of  "relationship"  was,  however,  of  the  other 
sort;  and  since  it  had  a  basis  in  the  phyvsical  laws  of  vibrating 
bodies,  it  naturally  was  described  in  terms  of  ratios  of  vibration 
rates.  Like  the  phenomenon  of  consonance  with  which  it  is 
closely  allied,  direct  "relationship"  seemed  to  be  dependent 
upon  the  partial  identity  of  overtones  which  exists  among 
"related  "tones. 

What  now  is  the  psychological  phenomenon  of  which  these 
physical  facts  seem  to  be  the  origin?    In  what  way  does  one's 

•  H.  Helmholtz,  5e«jo/iow5  £>/ r<7«e,  tr.  by  Ellis,  1895,  256  and  350. 


STUDIES  IN  MELODY.  9 

experience  of  a  pair  of  "related"  tones  differ  from  that  of  a 
pair  of  "unrelated"  tones?  The  difference  is  easily  felt,  but 
difficult  to  put  into  words.  I  shall  here  merely  quote  some 
more  or  less  descriptive  phrases  from  the  records  of  my  observ- 
ers. When  two  "  related  "  tones  are  heard  in  succession  they  are 
felt  to  'cohere',  to  'belong  together',  to  'articulate',  to  'form 
parts  of  a  larger  whole.'  "Unrelated"  tones  do  not  so  behave. 
Rather  they  are  felt  to  'fall  apart',  to  'be  unrelated';  'they  do 
not  seem  to  belong  to  the  same  melody.'  Tones  at  an  interval 
of  a  major  third  exhibit  a  strong  melodic  "relationship."  If 
the  interval  is  increased  by  a  quarter  of  a  tone  the  "relationship" 
disap  pears.  This  phenomenon  of '  'relationship' '  is  not  to  be  con- 
fused with  that  of  consonance.  The  dissonant  major  second,  for 
instance,  is  an  interval  whose  tones  exhibit  melodic  "relation- 
ship. "  What  the  significant  connection  is  which  exists  between 
melodic  "relationship"  and  consonance  will  be  pointed  out 
later. 

Another  type  of  relation  which  exists  between  the  successive 
tones  of  a  melodic  interval  may  be  called  the  relation  of  pitch 
distance.  As  regards  their  pitch  all  tones  range  themselves  in 
a  one-dimensional  series,  as  higher  or  lower;  and  the  relative 
position  of  two  tones  in  this  series  finds  its  conscious  represen- 
tative in  this  feeling  of  pitch  distance.  Thus,  the  tone  g'  is 
felt  to  be  at  a  certain  pitch  distance  from  c' ;  while  its  distance 
from  d'  is  felt  to  be  not  so  great.  It  is  at  once  perceived  that 
one's  consciousness  of  the  distance-relation  between  two  tones 
is  clearly  distinguishable  from  one's  consciousness  of  their  con- 
sonance or  of  their  "relationship." 

It  will  be  found  useful  to  distinguish  'definite'  from  what 
may  be  called  'indefinite'  pitch  relations.  The  former  are  char- 
acteristic of  all  melodies  which  employ  the  definite  intervals  of 
a  fixed  scale.  Some  kind  of  '  indefinite '  pitch  relation  must  be 
experienced  by  that  peculiar  type  of  unmusical  person  who  has 
no  exact  sense  for  intervals,  but  who  enjoys  hearing  himself 
sing,  and  who  can  sing  simple  melodies  in  perfect  time,  and  with 
so  much  sense  for  pitch  relations  as  is  shown  in  ascending  when 
the  melody  should  ascend,  and  then  descending  when  the 
course  of  the  melody  takes  a  downward  turn.    The  pitch-out- 


lO  W.  VAN  DYKE  BINGHAM. 

line  or  melodic  curve  of  his  song  corresponds  in  a  vague,  gen- 
eral way  with  the  pitch-outline  of  the  melody  imitated,  and  in-so- 
far  it  betrays  some  kind  of  a  sense  for  pitch  relationship.  These 
'indefinite'  pitch  relations  are  characteristic  of  certain  primi- 
tive melodies.  1  They  also  are  of  vast  importance  in  the  so-called 
melodies  of  speech.  Indeed,  the  infinite  variety  of  delicately 
expressive  inflections  which  enrich  our  spoken  intercourse  must 
be  recognized  as  based  upon  pitch  relations  of  this  'indefinite' 
kind.  The  gross  difi^erence  between  the  rising  interrogative 
inflection  and  the  falling  assertatory  is  the  most  obvious  example 
of  this  type  of  melodic  relationship.  The  mental  effects  pro- 
duced by  mere  rise  in  pitch  have  been  described  by  Meyer  in 
terms  of  effects  upon  the  attention. 

A  rise  in  pitch  causes  the  hearer's  attention  to  become  strained,  and 
the  more  so,  the  steeper  the  ascent,  if  I  may  use  this  expression.  A  fall 
in  pitch,  on  the  other  hand,  causes  a  relaxation  of  attention,  a  cessation  of 
mental  activity The  same  strain  and  relaxation  of  atten- 
tion is  to  be  found  in  music.  The  normal  end  of  a  mental  process  is, 
of  course,  characterized  not  by  strained,  but  by  relaxed  attention;  for 
strained  attention  means  continued  mental  activity.  It  is  natural 
therefore  that  a  melody  ends  with  a  falling  inflection.     .     .     .     ^ 

We  shall  have  occasion  frequently  to  refer  to  the  significance 
for  the  melody  problem  of  this  "phenomenon  of  the  falling 
inflection." 

§7.  If  one  carefully  examines  different  melodic  intervals  to 
discover  whether  there  may  not  be  still  other  types  of  relation, 
he  will  probably  disclose  to  himself  a  phenomenon  which  has 
received  much  attention  at  the  hands  of  certain  writers.  He  will 
notice  that  many  melodic  intervals  exhibit  a  peculiar  character 
which  shows  itself  as  a  tendency  for  us  to  prefer  one  of  the  two  tones 
as  an  end  tone.  The  interval  of  the  minor  third,  whose  tones 
have  the  vibration  ratio  of  5:6,  possesses  no  such  attribute: 
one  acquiesces  indifferently  in  either  the  upper  or  the  lower  as  a 
final  tone.  Neither  tone  has  any  very  positive  characteristics 
of  finality  about  it.  Not  so,  however,  with  the  perfect  fifth 
(2:3).    If  one  hears  it  as  an  ascending  interval,  he  is  dissatis- 

*  Cf.,  B.  I.  Gllman,  "Hopi  Songs,"  Jour,  of  Am.  Ethnol.  and  Archeol.  1908,  5, 
14  and  224. 

^  Am.  Jour.  Psych.,  1903,  14,  456. 


STUDIES  IN  MELODY.  II 

fied,  uneasy,  and  under  more  or  less  tension  until  he  hears  the 
first  tone  over  again.  But  if  it  is  a  descending  fifth  which  he  hears 
there  is  acquiescence,  satisfaction,  repose,  and  no  desire  to  hear 
the  first  tone  a  second  time.  One  may  say  that  one  of  these 
tones  stands  to  the  other  in  the  relationship  of  'tonic',  or  end- 
tone.  This  aspect  of  musical  intervals  will  be  called  by  the 
present  writer  their  melodic  trend. 

Observation  of  this  phenomenon  as  it  shows  itself  in  inter- 
vals of  relatively  simple  vibration  ratio  has  led  some  theorists, 
notably  Lipps  and  his  followers,  to  attach  great  importance  to 
the  2  ratio.  They  find,  for  example,  that  the  trend  of  the  fourth 
(3:4)  is  very  decidedly  toward  its  upper  tone  as  a  final  tone;  of 
the  major  third  (4:5),  toward  the  lower;  while  the  minor  third 
(5:6)  exhibits  no  noticeable  trend  whatever.  The  trend  of  the 
major  second  (8 19)  is  toward  the  lower,  and  of  the  minor  second 
(15:16)  toward  the  higher  tone.  Among  the  wider  intervals, 
where  the  reader  may  perhaps  feel  that  the  phenomenon  is  not 
always  so  distinctly  and  unambiguously  manifest,  it  is  never- 
theless held  that  the  minor  sixth  (5:8)  and  the  minor  seventh 
(9:16)  trend  upward  and  the  major  seventh  (8:15)  downward, 
while  the  major  sixth  (3 :5)  shows  no  trend  toward  either  upper 
or  lower  tone.^ 

It  will  be  seen  that  in  the  case  of  every  one  of  these  'pure' 
intervals  the  trend  is  toward  that  tone  whose  rate  is  a  pure 
power  of  2 ;  2  always  becomes  the  tonic.  Where  neither  rate  is 
a  pure  power  of  2,  no  trend  is  discovered.  These  phenomena 
have  been  grouped  by  Lipps  under  what  he  calls  the  '  law  of  the 
number  2. ' 

Kiirzer  gesagt: — Treffen  Tone  zusammen,  die  sich  zueinander  ver- 
halten  wie  2°:  3,  5,  7  usw.,  so  besteht  cine  natiirliche  Tendenz  der  letz- 
teren  zu  den  ersteren  hin;  es  besteht  eine  Tendenz  der  inneren  Bewegung, 
in  den  ersteren  zur  Ruhe  zu  kommen.  Jene  "suchen"  diese  als  ihre 
natiirliche  Basis,  als  ihren  natiirlichen  Schwerpunkt,  als  ihr  natiirliches 
GraKdtationszentrum. 

Dies  ist  naturgemass  um  so  mehr  der  Fall,  je  kleiner  das  (n)  ist. 

*  These  statements  of  t3T)ical  trends  are  not  completely  in  harmony  with  the  results 
of  the  experiments  described  below.  Differences  are  most  in  evidence  in  the  case  of 
the  major  and  minor  sevenths.     See  p.  25  _^. 


12  W.  VAN  DYKE  BINGHAM. 

(n)  ist  aber  am  kleinsten,  wenn  es  gleich  o  ist.  Und  2°  ist  gleich  i.  D.  h. 
die  vollkommenste  Ruhelage  und  das  letzte  Gravitationszentrum 
solcher  Tone  bleibt  immer  der  absolute  Grundrhythmus/ 

Upon  this  law  of  the  compelling,  dominating  character  of 
the  2  ratio,  together  with  the  principle  that  melodic  "relation- 
ship" is  closer  the  simpler  the  ratios,  Lipps  grounds  his  theory 
that  a  melody  is  a  structure  which  gains  its  esthetic  unity 
through  the  subordination  of  all  its  elements  to  one  over-master- 
ing ground-ratio,  the  tonic.  This  theory  has  been  elaborated, 
in  its  application  to  modern  European  music,  in  admirable 
detail  by  Weinmann,^  and  defended  vigorously  by  the  author 
himself.^ 

In  undertaking  to  explain  why  this  phenomenon  of  melodic 
trend  toward  the  power  of  2  should  manifest  itself,  Lipps  makes 
one  fundamental  assumption,  the  assumption 

that  to  the  rhythm  of  the  physical  vibrations  which  generate  a  tone 
there  corresponds  an  analogous  rhythm  in  the  accompanying  processes 
of  tone-sensation,  or  in  the  accompanying  change  of  psychic  or  central 
conditions;  that  thus  the  psychic  or  central  process  of  tone  sensation  is 
separated  into  a  succession  of  elements  or  elementary  partial  processes 
analogous  to  the  succession  of  physical  partial  processes,  i.  e.,  to  the  single 
sound  waves.* 

Such  a  correspondence  between  the  nature  of  central  proces- 
ses and  the  physical  processes  which  arouse  them,  Lipps  has 
found  it  necessary  to  postulate  not  merely  in  the  realm  of  audition, 
but  throughout  the  range  of  sensory  experience.  Esthetic 
pleasure  results  from  inner  harmony  of  our  mental  (or  cen- 
tral) energies.  A  color-contrast  is  beautiful  if  there  is  a  sub- 
conscious apprehension  of  the  simplicity  of  the  combination  of 
the  ether  vibrations. 

In  the  present  state  of  total  ignorance  with  reference  to  the 
intimate  nature  of  central  processes  no  attempt  can  be  made 

1  Lipps.  Psychologische  Studien,  2  Aufl.,  1905,  195.  An  identical  formulation  is 
given  in  his  Grundlegung  der  Aesthetik,  1903,  465. 

*F.  Weinmann,  "Zur  Structur  der  Melodie.  Zeits.  f.  Psychol.,  1904,  js,  340-379 
and  401-453. 

'  Cf.,  especially,  Psychologische  Studien,  193^. 

*  Zeits.  f.  Psychol.,  1902,  27,  228. 


STUDIES  IN  MELODY.  13 

either  to  establish  or  to  disprove  such  an  assumption.  By 
those  who  cannot  follow  Lipps  in  his  bold  hypothesis,  his  theory 
of  the  number  2  must  be  viewed  merely  as  a  description,  not 
an  explanation,  of  the  facts. 

Weinmann  undertakes  to  buttress  this  theory  of  the  basic 
nature  of  'duality'  in  vibration-ratios  by  reminding  the  reader 
that  '  double  rhythm '  is  the  original  rhythm,  the  simplest,  the 
most  natural,  etc.^  But  this  is  an  swgument  from  sheer  analogy; 
for  the  experience  of  rhythm  in  the  ordinary  sense  of  the  word 
has  nothing  whatever  in  common  with  the  unperceived  micro- 
rhythm  of  Lipps'  assumption.  One  is  a  phenomenon  open  to 
introspection,  observation  and  experimental  study:  the  other  is 
hidden,  unknown,  hypothetical. 

Even  though  one  may  not  relish  such  a  theory  as  that  of 
Lipps  and  Weinmann,  and  though  one  may  be  inclined  to  doubt 
the  adequacy  of  their  formulation  of  the  facts  by  means  of  the 
law  of  the  number  2,  nevertheless  the  phenomena  of  melodic 
trend  remain  and  must  be  reckoned  with.  Why  is  it  that  some 
melodic  intervals  seem  to  end  better  on  the  upper  tone  and  others 
on  the  lower,  while  with  still  others  it  is  a  matter  of  indifference 
which  of  the  two  tones  comes  last?  Why  is  a  rising  fourth  more 
'complete'  than  a  rising  fifth?  Why  does  an  ascending  major 
second  create  a  demand  to  hear  the  first  tone  over  again,  while 
an  ascending  minor  second  does  not? 

§8.  No  further  attempt  will  here  be  made  to  enumerate  with 
greater  completeness  the  various  mental  phenomena  which 
flow  from  the  facts  of  pitch  relationship.  Only  those  have  been 
mentioned  which  are  of  especial  significance  for  these  studies: 
pitch  distance,  definite  melodic  "relationship,"  indefinite 
pitch  relations,  consonance,  melodic  trend,  the  phenomenon 
of  the  falling  inflection.  We  shall  later  have  occasion  to  ask 
which  of  these  phenomena  are  primary  and  which  secondary  or 
derived. 

Our  survey  of  the  factors — of  pitch,  duration,  clang-color 
and  intensity  relations — which  contribute  to  the  structure  of 
a  melody,  makes  possible  a  more  definite  formulation  of  the 
limited  purpose  of  these  studies, 

'  op.  c,  342. 


S4  W.  VAN  DYKE  BINGHAM. 

How  the  pitch  relations  of  a  series  of  discrete  musical  sounds 
may  operate  to  weld  these  sounds  into  the  organic  whole  which 
we  perceive  as  a  melody, — this  is  the  core  of  the  melody  problem, 
and  to  this  primary  phase  of  the  subject  our  present  investiga- 
tion will  be  strictly  limited.  To  this  end  we  shall  consider 
pitch  alone,  and  abstract  as  far  as  possible  from  all  considera- 
tions of  rhythmic  figuration,  accent,  force,  tempo,  tone  quality, 
etc.,  although  these  various  factors  would  all  demand  attention 
in  any  account  of  the  melody  problem  which  aimed  at  complete- 
ness. 


PART  II. 

THE  PHENOMENA  OF  MELODIC  "RELATIONSHIP"  AND  OF  MELODIC 

TREND. 

§9.  The  reports  of  previous  experimentation  specifically 
directed  toward  the  melody  problem  are  few  in  number. 

One  of  the  most  original  and  suggestive  workers  has  been 
Professor  Meyer,  and  a  survey  of  his  contributions  will  serve  to 
bring  our  own  problem  more  clearly  to  view. 

The  first  of  Meyer's  experimental  investigations^  led  him  to 
reject  the  theory  of  the  diatonic  scale,  and  to  develop  a  new 
theory  of  melody.  He  used  a  reed  organ  specially  constructed 
so  that  in  playing  a  melody  the  performer  was  enabled,  for  each 
note  of  the  printed  score,  to  select  any  one  of  two  or  three  tones 
of  nearly  the  same  pitch.  Thus  after  repeated  trials  he  could 
determine  precisely  what  intonation  of  any  particular  melody 
was  most  satisfactory.^ 

Meyer  published  his  analysis  of  some  thirteen  melodies,  giv- 
ing the  intonation  of  each  which  seemed  to  him  to  be  the  best. 
These  include  melodies  of  folk  songs  and  chorals  as  well  as  melo- 
dies from  well  known  classical  compositions.  The  reader  is  not 
surprised  to  find  that  the  preferred  intonation  does  not  coincide 
with  that  of  "equal  temperament;"  but  neither  does  Meyer  find 
that  the  melodies  are  most  satisfactory  when  played  in  the  justly 
intoned  diatonic  scale  familiar  to  musical  theorists.  To  be  sure, 
in  the  simpler  melodies,  most  of  the  pitches  in  the  preferred 
intonation  correspond  exactly  with  the  pitches  when  the  melody 
is  played  in  accordance  with  the  diatonic  scale.  Some  marked 
exceptions  appear,  however.     Meyer  finds,  for  instance,  that 

^M.  Meyer:  "Elements  of  a  Psychological  Theory  of  Melody."  Psych.  Rev., 
1900,  7,  241-273.  Reprinted  with  revisions  and  additions  in  "Contributions  to  a 
Psychological  Theory  of  Music,"  Univ.  of  Missouri  Studies,  1901,  /,  1-80. 

*  A  description  of  the  instrument,  with  diagram  of  arrangement  of  keys  on  the  manual 
is  found  in  the  Zeits.f.  Psychol.  1903,  jj,  292. 


1 6  W.  VAN  DYKE  BINGHAM. 

the  'fourth'  is  preferred  flatter  and  the  'sixth'  sharper  than 
diatonic  intonation  demands.  To  render  the  nature  of  these 
differences  more  clear,  reference  may  be  made  to  the  accom- 
panying table. 

TABLE  NO  1. 


/ 


^  ,.    r   •.  u    •   J-    f  I    9/8    s/4     4/3     3/2     5/3     15/8      2 

Ratios  Of  pitches  in  dia-         /g     ^^/       ^^/^^         ^/g       ^^/^         ^/g     ^^/ij 

tonic  scale  <  .«  ^^  ^e 

[24       27         30  32  36  40  45  40 

Some       corresponding  f  i       9/8       5/4     2l/l6        3/2      27/16        15/8  2 

pitches  from  Meyer's  \     9/8     10/9     21/20         8/7         9/8       10/9     16/15 
Complete  Scale.  [16       18         20  21  24  27  30  32 

Diatonic  scale  48       54        60  64  72  80  90  96 

Meyer's  48       54        60  63  72  81  90  96 

The  first  line  of  fractions  shows  the  ratio  between  the  vibration 
rate  of  each  note  of  the  diatonic  scale  and  the  vibration  rate  of  the 
key  note.  Reducing  these  fractions  to  a  common  denominator, 
we  obtain  as  the  resulting  numerators  the  numbers  in  the  third 
row  of  the  table.  These  are  the  numbers  usually  employed  to 
express  the  relative  pitch  of  the  notes  in  the  diatonic  scale.  (The 
ratio  between  the  vibration  rate  of  each  note  and  that  of  the 
next  note  in  the  scale  is  given  in  the  second  line  of  fractions). 

For  comparison  with  these,  I  have  selected  from  Meyer's 
'Complete  Scale'  those  notes  which  are  used  in  the  simpler 
melodies  (see  lines  4,  5  and  6  of  the  table). 

It  is  to  be  noted,  first,  that  the  ratios  in  the  diatonic  scale 
involve  no  prime  number  but  2,  3,  and  5,  whereas  the  other 
scale  employs  the  number  7  in  its  fourth.  Thus,  to  tune/  in  the 
key  of  c  one  would  not  tune  it  a  perfect  fourth  above  c,  but 
would  tune  it  at  an  interval  of  an  harmonic  or  sub-minor  seventh 
(74)  above  the  g  below.  Moreover  the  denominators  of  all 
eight  ratios  from  the  newer  scale  are  pure  powers  of  2  whereas 
this  is  not  the  case  with  the  fourth  and  sixth  of  the  diatonic 
scale.  The  amount  of  difference  in  pitch  which  is  involved  is 
shown  in  the  last  two  lines  of  the  table  where  the  ratios  of  the 
two  scales  are  reduced  to  a  common  denominator  for  compari- 
son. 


STUDIES  IN  MELODY.  17 

To  understand  the  significance  which  attaches  to  these  differ- 
ences, and  other  more  marked  differences  in  intonation  which 
come  to  light  in  the  more  complex  melodies,  it  is  necessary  to 
examine  two  "laws  of  melody"  which,  if  one  follows  Meyer,  lie 
at  the  basis  of  musical  theory. 

§10.  The  first  of  Meyer's  laws  of  melody  may  be  called  the 
law  of  melodic  '^relationship : "  Only  tones  which  are  "related, " 
directly  or  indirectly,  can  belong  to  the  same  melody.  The 
second,  a  law  of  melodic  trend,  is  similar  to  Lipps'  law  of  the 
number  2. 

We  will  give  Meyer's  own  formulation  of  what  he  means  by 
the  term  "relationship." 

When  we  hear  successively  two  tones,  the  vibration  rates  of  which  are 
to  each  other  as  2:3,  or  briefly  speaking,  the  tones  2  and  3,  we  notice 
something  not  describable,  which  I  shall  call  the  relationship  of  these 
tones.  To  understand  what  is  meant  hereby,  the  reader  may  listen  to 
the  successive  tones  7  and  11  or  11  and  10,  in  which  cases  he  will  notice 
that  the  two  tones  have  no  relation  at  all  to  each  other.* 

It  is  a  fundamental  contention  with  Meyer, — a  contention 
that  will  demand  our  critical  scrutiny, — that  this  psychological 
quality  called  "relationship"  attaches  only  to  pairs  of  tones 
whose  ratios  are  expressible  in  simple  fractions  involving  no 
prime  number  above  7. 

That  no  relationship  at  all  is  to  be  observed  with  tones  represented 
by  the  prime  numbers  11,  13,  17,  19,  etc.,  leads  to  the  conclusion  that 
only  tones  represented  by  the  prime  numbers  i,  2,  3,  5,  7,  and  their  com- 
posites possess  that  psychological  property.^ 

This  leads  to  the  theory  of  what  Meyer  names  '  the  complete 
scale.'  Since  none  but  related  tones  can  belong  to  the  same 
melody,  and  since '  'relationship"  seems  to  exist  only  between  tones 
represented  by  products  of  2,  3,  5,  and  7,  the  complete  musical 
scale,  or  the  series  of  all  the  tones  which  may  occur  in  a  single 
melcidy,  is  represented  by  the  infinite  series  of  all  products  of 
the  powers  of  2,  3,  5,  and  7  (p.  249).  The  beginnings  of  such  a 
scale,  containing  so  many  of  these  related  products  as  were  found 

*  Meyer:  PiycA.  Rev.,  1900,  246. 

*  Op.  c,  247. 


l8  W.  VAN  DYKE  BINGHAM. 

to  be  needed  in  the  analysis  of  the  melodies  he  studied,  are 
given  by  Meyer  in  tabular  form. 

In  maintaining  that  the  7  ratio  exhibits  the  fundamental 
melodic  qualities  and  must  not  be  excluded  from  musical  theory, 
Meyer  takes  sharp  issue  with  traditional  treatments  of  the  sub- 
ject. Lipps  and  his  followers  who  have  done  more  than  anyone 
else  to  place  the  theory  of  melody  on  a  basis  of  exact  descriptive 
formulation  find  no  need  of  ratios  involving  prime  factors 
larger  than  5.  Other  writers,  as  Helmholtz,  Gumey  and  Stumpf 
have  also  been  content  with  the  theory  of  the  diatonic  scale, 
a  scale  whose  ratios  employ  the  numbers  2,  3,  and  5,  but  not  the 
number  7.  Against  these,  Meyer  brings  the  charge  that  they 
have  been  influenced  primarily  by  considerations  involving  the 
phenomena  of  harmony,  and  have  failed  to  point  out  what  facts 
observable  in  melody  justified  them  in  excluding  the  number  7. 
The  facts  as  he  finds  them  are  that  such  melodic  intervals  as 
the  sub-minor  seventh  (4:7)  the  sub-minor  fifth  (5:7)  the  sep- 
timal  second  (7:8),  etc.,  do  possess  the  pyschological  quality  of 
"relationship;"  and  what  is  of  more  weight,  he  finds  that  melodies 
played  in  his  so-called  complete  scale,  which  admits  the  7  ratio, 
are  preferred  to  the  same  melodies  played  according  to  the 
diatonic  scale. 

Meyer  has  been  subjected  to  criticism  for  publishing  his 
experiments  and  basing  an  elaborate  theory  upon  them,  when 
the  judgments  of  preference  recorded  are  apparently  those  of  a 
single  observer,  namely,  the  author  himself.  Meyer  admits  the 
force  of  these  criticisms,  but  insists  that  even  so  much  of  induc- 
tion and  carefully  systematized  observation  as  this  report  of  his 
studies  embodied,  has  more  claim  upon  the  attention  of  a  scientific 
reader  than  all  the  great  mass  of  writing  upon  musical  theory 
which  has  no  scientific,  inductive  basis  whatever. 

How  does  Meyer  account  for  the  phenomena  of  melodic 
"relationship?"  How  does  he  explain  the  fact  that  we  feel  the 
tones  2  and  3  to  be  "related"  and  the  tones  11  and  10  "unre- 
lated?" In  contrast  to  Lipps  he  does  not  attempt  to  account 
for  the  facts.  On  the  other  hand  he  frankly  admits  that  he  is  not 
offering  an  explanation  of  the  melody  phenomena:  for  this,  as 
well  as  for  an  explanation  of  the  facts  of  consonance  we  must 


STUDIES  IN  MELODY.  19 

await  further  light  upon  the  nature  of  neural  activity  and  the 
action  of  the  sense  organs.  All  that  Meyer  is  attempting,  then, 
is  to  comprehensively  describe  the  facts. 

His  first  step  toward  this  descriptive  formulation  has  already 
been  mentioned.  As  a  result  of  his  examination  of  the  phe- 
nomenon of  melodic  "relationship"  he  decided  that  all  cases  of 
"relationship"  are  capable  of  being  expressed  in  relatively 
simple  fractions  involving  no  prime  factors  except  2,  3,  5,  and  7; 
and  consequently  the  'complete  scale'  is  limited  to  tones  ex- 
pressed in  these  numbers  and  their  compounds.  The  second 
step  is  the  formulation  of  a  law  of  melodic  trend  similar  to,  but 
not  identical  with,  that  of  Lipps: 

When  one  of  two  related  tones  is  a  pure  power  of  2,  we  wish  to  have 
this  tone  at  the  end  of  our  succession  of  related  tones,  our  melody.^ 

Expanded  to  cover  melodies  of  more  than  two  tones,  the  law 
assumes  the  following  form: 

No  hearer  is  satisfied  if  after  having  heard  once  or  more  often  the 
tonic  2  he  does  not  find  2  finally  at  the  end  of  the  melody.' 

In  the  elaboration  of  his  theory  Meyer  utilizes  two  additional 
principles.  One  of  these  is  that  among  "related"  tones  there 
exist  different  degrees  of  "relationship."  The  other  principle 
is  that  of  all  those  intervals  which  possess  a  certain  "relation- 
ship" we  have  a  decided  preference  for  the  smallest.  The 
detailed  development  of  the  theory  based  upon  these  principles 
we  shall  not  here  undertake  to  summarize,  but  its  foundations 
we  must  pause  to  examine  more  closely.  It  is  obvious  that 
there  is  need  of  conclusive  evidence  supporting  the  basic  propo- 
sition upon  which  the  theory  is  erected,  the  proposition  that 
tones  representable  by  the  prime  numbers  up  to  and  including 
7  alone  exhibit  "relationship." 

As  evidence  Meyer  presents,  as  we  have  seen,  two  groups  of 
facte,  one  derived  from  an  examination  of  separate  intervals 
and  one  from  observation  of  the  use  in  actual  melodies  of  the  7 
ratio.     In  both  cases,  as  Wead^has  pointed  out  in  his  penetrat- 

^  University  of  Missouri  Studies,  i,g. 
*  L.  c,  24. 
C.  K.  Wead,  Psychological  Review,  1900,  7,  400. 


20  W.  VAN  DYKE  BINGHAM. 

ing  review  of  Meyer's  work,  the  judgments  recorded  are  appar- 
ently those  of  a  single  observer,  and  he  a  man  of  harmonic 
training.  What  indication  is  there  that  one  who  had  never 
become  familiarwith  anything  comparable  with  our  European 
harmonic  musical  system  would  experience  these  elementary 
"relationships?"  "Nothing,"  says  Wead,  "can  be  more  cer- 
tain historically  than  that  these  relationships  have  been  unrec- 
ognized by  most  of  the  men  throughout  the  ages  who  have 
concerned  themselves  about  music."  One  cannot  avoid  ask- 
ing the  question  whether  Meyer's  deductions  necessarily  hold 
for  hearers  of  melody  other  than  those  who,  like  himself,  have 
long  experienced  the  associations  of  modern  European  music. 

A  somewhat  similar  question  arises  regarding  the  effects  of 
practice  in  detecting  these  melodic  "relationships." 

Meyer  leads  us  to  understand  that  only  after  long  and 
careful  observation  did  he  decide  that  5:7  and  7:8  exhibit 
"relationship."  In  another  connection  he  proves*  that  "rela- 
tionships" not  detected  at  first  come  later  to  be  felt,  upon 
greater  familiarity.  This  seems  to  place  him  in  a  dilemma. 
May  it  not  be  that  the  familiarity  breeds  the  "relationship?" 

It  would  not  be  rash  to  hazard  that  if  Meyer  had  chanced  to 
spend  his  early  years  in  the  Scottish  Highlands  it  would  never 
have  occurred  to  him  to  exclude  1 1  while  admitting  7  among  the 
prime  factors  of  his  'complete  scale;'  for  in  listening  to  the  bag- 
pipe he  would  have  become  accustomed  to  the  interval  11  :i2,^ 
would  have  learned  to  recognize  it  accurately,  and  to  feel 
"relationship"  between  11  and  12  as  truly  as  between  15  and 
16,  or  7  and  8. 

As  long  as  the  question  remains  unsettled  regarding  the 
inclusion  or  exclusion  of  7,  1 1,  or  any  other  ratio  in  making  up 
the  list  of  elementary  "relationships,"  a  certain  doubt  will 
remain  regarding  the  validity  of  Meyer's  experiments  on  the 
intonation  of  actual  melodies;  for,  in  selecting  the  preferred 
pitches  the  observer's  choice  of  alternatives  for  each  note,  it 
will  be  remembered,  was  limited  to  the  two  or  three  tones 

*  See  below,  p.  40. 

*  C/.,  A.  J.  Ellis:  "  On  the  Musical  Scales  of  Various  Nations,  "/ottrna/  of  the  Society 
of  Arts,  London,  1885, 33,  499. 


STUDIES  IN  MELODY.  2  I 

available  from  the  scale  constructed  out  of  products  of  2,  3,  5, 
and  7. 

Instead  of  attempting  here  to  settle  this  issue,  let  us  ask 
some  further  questions  with  reference  to  Meyer's  two  main 
contentions.  Is  it  true  that  only  intervals  the  ratios  of  whose 
vibration  rates  are  expressible  in  small  prime  numbers  mani- 
fest the  psychological  quality  of  "relationship?"  Is  it  a  fact 
that  of  two  "related"  tones  whose  ratio  can  be  thus  expressed, 
the  hearer  always  prefers  cis  an  end-tone  that  one  which  is  a  pure 
power  of  2  ? 

§11,     First  let  us  consider  the  fact  of  melodic  "relationship. " 

The  major  third  is  an  interval  which  exhibits  the  character 
of  * '  relationship ' '  very  unambiguously.  This  is  an  interval  whose 
tones  have  the  vibration  ratio  of  4:5.  Now,  what  is  the  effect 
when  we  listen  to  an  interval  just  barely  wider  than  this,  say 
the  interval  400:501?  It  so  happens  that  this  interval  exhibits 
the  "relationship"  more  clearly,  if  anything,  than  4:5  did,^ 
although  it  is  so  nearly  the  same  interval  that  those  without 
special  training  cannot  tell  the  two  apart.  Suppose  this  inter- 
val to  be  made  a  trifle  larger  yet,  so  that  it  has  the  ratio  400 1504. 
Do  the  tones  suddenly  lose  their  character  of  "relationship?" 
One  would  hardly  expect  them  to  do  so.  Precisely  what  does 
occur  is,  that  as  the  width  of  the  interval  is  gradually  increased 
it  begins  to  change  somewhat  in  character;  but  it  remains  a 
major  third, — not  a  satisfactory  third  to  be  sure,  but  neverthe- 
less a  third  with  the  characteristic  ''relational  attributes  of  that 
interval, — until  it  reaches  nearly  to  the  middle  of  the  zone 
which  divides  the  major  third  from  a  perfect  fourth. 

The  experimental  evidence,  if  any  is  required,  in  support  of 
these  statements,  is  easily  obtained.  The  procedure  adopted 
by  the  writer  was  to  determine  the  effect  produced  upon  the 
feeling  of  "relationship"  by  gradual  but  supra-liminal  varia- 
tions in  the  size  of  a  melodic  interval.  Between  the  b  and  c' 
of  k  harmonium  six  reeds  were  interpolated,  giving  seven  inter- 
vals, each  of  a  magnitude  of  about  16  cents  {i.  e.,  hundredths  of 

^  Stumpf  and  Meyer  found  that  all  of  the  consonant  intervals  larger  than  a  minor 
third  are  preferred  too  large.  C.  Stumpf  and  M.  Meyer,  "Maassbestimungeniiber 
die  Reinheit  consonanter  Intervalle."    Zeits.f.  Psychol.,  1898, 18, 321. 


W.  VAN  DYKE  BINGHAM. 


an  equally  tempered  semi- tone).  Such  an  interval  in  this  region 
of  the  scale  means  a  difference  in  pitch  of  scarcely  more  than  two 
vibrations.  It  was  thus  possible  to  play  any  desired  diatonic 
interval  and  also  any  one  of  half  a  dozen  intervals  intermediate 
in  magnitude  between  it  and  the  next  larger  interval.  Only  the 
major  third  and  the  fourth  were  tested.  The  method  was  with- 
out knowledge.  The  twelve  observers  were  already  familiar 
with  the  phenomena  of  "relationship"  and  finality  in  two- tone 
combinations.  They  were  ignorant  of  the  nature  and  purpose 
of  the  experiment.  The  observer  was  asked  whether  or  not  the 
two  tones  played  were  "related,  "and  if  the  response  was  in  the 
affirmative  the  further  question  was  put,  regarding  the  com- 
pleteness or  incompleteness  of  the  two-tone  group. 

It  was  found,  with  each  of  the  twelve  observers,  that  the 
characteristic  feeling  of  "relationship"  was  nearly  always  still 
present  when  the  interval  had  been  increased  (or  diminished) 
32  cents,  (a  third  of  an  equally  tempered  semi- tone).  The 
characteristic  feeling  for  the  upper  or  the  lower  as  an  end-tone 
also  remained.  An  alteration,  however,  of  48  cents  (roughly  a 
quarter  of  a  tone)  destroyed  the  feeling  of  "relationship"  in 
74  per  cent  of  the  96  judgments. 

In  general,  when  a  pure  interval  is  gradually  modified  its 
characteristic  melodic  qualities  remain  long  after  the  interval 
has  lost  the  characteristic  qualities,  e.  g.  of  consonance,  which  it 
manifests  when  its  two  tones  are  heard  simultaneously  instead 
of  in  succession.  This  fact  ought  to  be  of  weight  for  any  theory 
of  melody  which  lays  emphasis  upon  the  psychological  quality 
of  felt  "relationship."  Since  the  ratio  3:4  has  no  monopoly 
upon  the  characteristic  "relational"  qualities  of  the  fourth,  but 
is  rather  only  a  modal  ratio  about  which  cluster  an  immense 
number  of  larger  and  smaller  ratios  manifesting  in  some  meas- 
ure identically  the  same  psychological  qualities,  the  use,  with- 
out qualification,  of  the  symbol  3:4  to  represent  that  particu- 
lar kind  of  "relationship' '  is  misleading. 

What  is  true  in  this  respect  regarding  the  facts  of  "relation- 
ship" is  of  course  equally  true  regarding  the  facts  of  finality  or 
melodic  trend. 

It  may  be  urged  that  we  are  here  confronted  simply  with  the 


STUDIES  IN  MELODY.  23 

common  characteristic  of  perception,  the  modification  of  sen- 
sory data  by  central  processes  so  that  these  data  may  be  apper- 
ceived  to  the  nearest  available  norm.  Such  tests  as  the  above 
then  would  merely  measure  the  tendency  of  the  listener  to  hear 
different  nearly  equal  intervals  as  the  same  pure  interval,  and 
do  not  prove  that  the  "relationship"  of  the  fourth  inheres  in 
any  other  ratio  than  3:4. 

But  such  a  view  neglects  the  fact  that  when  we  are  listening 
to  an  interval  slightly  larger  than  3:4,  we  may  recognize  it  as 
larger  and  still  at  the  same  time  experience  the  feeling  of  "rela- 
tionship" characteristic  of  the  fourth.  The  "relationship," 
in  other  words,  inheres  not  merely  in  the  interval  3  4,  but  also 
in  intervals  recognizably  larger  or  smaller  than  the  justly 
intoned  perfect  fourth. 

§12.  We  shall  not,  however,  press  this  consideration.  In- 
stead we  shall  leave  in  abeyance  the  question  regarding  the  range 
of  applicability  of  the  pure  powers  of  2  formula,  and  shall  seek, 
in  the  results  of  the  experiments  now  to  be  described,  the  answers 
to  certain  questions  with  reference  to  the  melodic  trend  in  inter- 
vals with  the  simplest  arithmetical  ratios, — the  intervals  in 
which  we  are  led  to  expect  that  the  phenomena  will  be  most  in 
evidence.  Does  experiment  establish  the  proposition  that  when 
one  of  two  related  tones  is  a  pure  power  of  2,  we  wish  to  have  this 
tone  at  the  end,  and  that  when  neither  of  the  related  tones  is  a 
pure  power  of  2,  no  preference  is  felt  for  either  as  an  end-tone? 
What  is  the  relative  strength  of  the  trend  in  different  two-tone 
combinations?  Do  the  simplest  ratios  exhibit  it  most  definitely? 
Do  all  observers  feel  it  alike? 

The  method  of  the  experiment  was  to  present  two  tones  in 
succession,  and  ask,  "Can  you  make  this  second  tone  a  final 
tone?    Does  this  melody  end?"^ 

The  following  series  of  ratios  was  used:  2:3,  5:6,  3:5,  15:16, 
45:64,  4:5,  9:16,  32:45,  8:9,  8:15,  5:8,  34.  This  series  was  given 
in  the  'double  fatigue  order,'  both  ascending  and  descending. 
Ten  of  the  twelve  ratios  are  relatively  simple.    Two,  the  aug- 

*  At  the  time  when  these  experiments  were  planned,  the  experimenter  was  using 
the  term  'melody'  in  the  sense  in  which  Meyer  uses  it.  When  the  word  impHes  nothing 
except  "relationship,"  it  is  entirely  appropriate  to  speak  of  melodies  of  only  two  tones 


24  W.  VAN  DYKE  BINGHAM. 

men  ted  fourth  and  diminished  fifth  (32:45  and  45:64),  in- 
volve pure  powers  of  2  but  are  not  simple,  and  were  included 
for  purposes  of  comparison.  Heavy  Koenig  forks  mounted 
on  resonance  boxes  and  actuated  by  a  rubber  mallet  were  used 
as  the  source  of  sound.  Each  tone  was  sounded  for  five  seconds. 
The  range  of  pitch  was  limited  to  the  once  and  twice  accented 
octaves,  the  lowest  fork  being  the  middle  c'  of  256  d.  v.  and  the 
highest  the  g''  of  768  d.  v.  In  arranging  the  series  care  was 
taken  that  neither  of  the  tones  of  any  pair  belonged  to  a  tonality 
which  might  have  been  suggested  by  the  interval  preceding. 

Eight  persons  served  as  observers  in  this  series.  None  of 
them  would  be  classed  as  totally  unmusical,  and  none  of  them 
are  "musicians,"  yet  they  represent,  between  these  extremes, 
a  wide  range  of  musical  ability.  All  are  f  amilar  with  musical  nota- 
tion and  sing  or  play  some  from  note.  With  at  least  two  of  the 
observers,  there  is  a  lack  of  interest  in  music,  their  skill  at  the 
piano  being  a  mechanical  acquisition.  Three  of  the  observers 
confessed  to  an  acquaintance  with  the  elements  of  harmony 
and  musical  theory,  but  it  was  evident  upon  trial  that  their 
theoretical  knowledge  was  not  concrete  enough  to  exert  any 
influence  upon  their  immediate  judgments  of  musical  intervals. 
It  may  be  remarked  here  that  throughout  these  and  also  the  later 
experiments  the  observers  gave  unreasoned  judgments,  the 
introspective  records  on  this  point  confirming  the  opinion  of 
the  writer  based  upon  the  manner  of  their  replies.  All  the  ob- 
servers had  had  training  in  experimental  psychology. 

The  accompanying  table  gives  the  affirmative,  doubtful  and 
negative  judgments  of  each  of  the  eight  observers  with  respect 
to  each  of  the  melodic  intervals  used. 


STUDIES  IN  MELODY. 


25 


TABLE  NO.  2 
Two  Tones  Heard  in  Succession.    "Is  the  second  tone  a  final  tone?" 


INTERVAL 

OBSERVERS 

An. 

Td. 

Bl. 

Wl. 

Rn. 

Dg. 

Mc. 

Yo. 

TOTAL 

Minor  Second,  Ascending 

Affirmative 

2 

I 

2 

3 

4 

2 

I 

2 

17 

(iS:i6) 

Doubtful 

I 

0 

I 

0 

0 

0 

I 

I 

4 

Negative 

I 

3 

I 

I 

0 

2 

2 

I 

II 

Descending 

Affirmative 

I 

0 

0 

0 

0 

2 

I 

0 

4 

Doubtful 

0 

0 

2 

0 

0 

0 

I 

I 

4 

Negative 

3 

4 

2 

4 

4 

2 

2 

3 

24 

Major  Second,  Ascending 

Affirmative 

I 

0 

2 

0 

I 

0 

2 

0 

6 

(8:9) 

Doubtful 

2 

0 

0 

0 

I 

0 

I 

I 

S 

Negative 

I 

4 

2 

4 

2 

4 

I 

3 

21 

Descending 

Affirmative 

2 

2 

2 

3 

2 

3 

2 

4 

20 

Doubtful 

I 

I 

I 

0 

I 

0 

I 

0 

S 

Negative 

I 

I 

I 

I 

I 

I 

I 

0 

7 

Minor  Third,  Ascending 

Affirmative 

2 

0 

2 

0 

I 

0 

2 

0 

7 

(5:6) 

Doubtful 

I 

0 

2 

0 

I 

0 

0 

I 

S 

Negative 

I 

4 

0 

4 

2 

4 

2 

3 

20 

Descending 

Affirmative 

3 

0 

2 

I 

0 

1 

'    I 

2 

10 

Doubtful 

I 

0 

I 

0 

I 

0 

I 

0 

4 

Negative 

0 

4 

I 

3 

3 

3 

2 

2 

18 

Major  Third,  Ascending 

Affirmative 

3 

I 

0 

0 

0 

0 

0 

I 

S 

(4:5) 

Doubtful 

0 

I 

3 

0 

0 

0 

I 

2 

7 

Negative 

I 

2 

I 

4 

4 

4 

3 

I 

20 

Descending 

Affirmative 

3 

3 

4 

4 

4 

4 

4 

2 

28 

Doubtful 

I 

I 

0 

0 

0 

0 

0 

I 

3 

Negative 

0 

0 

0 

0 

0 

0 

0 

I 

I 

Perfect  Fourth  Ascending 

Affirmative 

4 

2 

\ 

3 

3 

4 

0 

I 

21 

(3:4) 

Doubtful 

0 

I 

0 

I 

I 

° 

I 

2 

6 

Negative 

0 

I 

0 

0 

0 

0 

3 

I 

S 

Descending 

Affirmative 

0 

0 

2 

0 

2 

0 

I 

3 

8 

"•  ^ 

Doubtful 

I 

2 

2 

2 

I 

I 

2 

0 

II 

Negative 

3 

2 

0 

2 

I 

3 

I 

I 

13 

Augmented  Fourth,    As- 

Affirmative 

0 

2 

2 

I 

I 

0 

0 

2 

8 

cending 

Doubtful 

0 

I 

2 

0 

0 

0 

0 

0 

3 

(32:4s) 

Negative 

4 

I 

0 

3 

3 

4 

4 

2 

21 

Descending 

Affirmative 

0 

0 

2 

0 

0 

I 

2 

I 

6 

Doubtful 

0 

I 

2 

0 

0 

I 

2 

I 

7 

Negative 

4 

3 

0 

4 

4 

2 

0 

2 

19 

26 


W.  VAN  DYKE  BINGHAM. 
Cont.  of  TABLE  No.  2 


INTERVAL 

OBSERVERS 

An. 

Td. 

Bl. 

WI. 

Rn. 

Dg. 

Mc. 

Yo. 

TOTAL 

Diminished     Fifth,    As- 
cending 
(45:64) 

Affirmative 

Doubtful 

Negative 

0 
0 
4 

I 
2 
I 

I 
2 
I 

0 
0 
4 

0 
0 
4 

0 
0 
4 

I 
0 
3 

0 

I 
3 

3 

S 

24 

Descending 

Affirmative 

Doubtful 

Negative 

0 
0 
4 

I 
I 
2 

I 

2 

I 

0 
0 
4 

0 

I 
3 

0 
0 
4 

I 
I 
2 

0 
0 
4 

3 

S 

24 

Perfect  Fifth,  Ascending 
(2:3) 

Affirmative 

Doubtful 

Negative 

I 
2 

I 

0 
2 
2 

2 
I 

I 

0 
0 
4 

2 

I 
I 

I 
I 
2 

I 
I 
2 

3 
0 
I 

ID 

8 

14 

Descending 

Affirmative 

Doubtful 

Negative 

4 
0 
0 

4 
0 
0 

4 
0 
0 

4 
0 
0 

4 
0 
0 

I 
2 

I 

I 

I 
2 

4 
0 
0 

26 

3 
3 

Minor  Sixth,  Ascending 
(5:8) 

Affirmative 

Doubtful 

Negative 

I 

3 
0 

4 
0 
0 

4 
0 
0 

2 
0 
2 

I 

2 

I 

0 

I 
3 

I 
0 
3 

I 
0 
3 

14 

6 

12 

Descending 

Affirmative 

Doubtful 

Negative 

0 
4 
0 

3 
0 
I 

2 

I 
I 

0 
0 
4 

I 
I 
2 

0 
0 
4 

0 

I 
3 

2 

I 
I 

8 

8 

16 

Major  Sixth,  Ascending 
(3:5) 

Affirmative 

Doubtful 

Negative 

I 

I 

2 

2 
0 
2 

3 
0 

I 

2 

I 
I 

I 
2 

I 

I 
0 
3 

I 
I 
2 

0 
0 
4 

II 

5 
16 

Descending 

Affirmative 

Doubtful 

Negative 

I 
2 

I 

2 
0 
2 

3 

I 
0 

I 
I 
2 

0 

3 

I 

I 
0 
3 

0 
2 
2 

0 
0 
4 

8 

9 

IS 

Minor  Seventh,  Ascend- 
ing 
(9:16) 

Affirmative 

Doubtful 

Negative 

0 
I 

3 

I 

3 
0 

3 

I 
0 

0 
0 
4 

0 
0 
4 

0 

0 
4 

I 
I 
2 

2 
0 
2 

7 
6 

19 

Descending 

Affirmative 

Doubtful 

Negative 

0 
2 
2 

2 
0 
2 

2 
2 
0 

0 
0 
4 

3 
0 
I 

0 
0 
4 

2 

I 
I 

0 
0 
4 

9 

S 
18 

Major  Seventh,  Ascend- 
ing 
(8:15)    ' 

Affirmative 

Doubtful 

Negative 

0 

I 
3 

2 

I 
I 

2 
2 
0 

I 
2 

I 

0 
0 
4 

0 
0 

4 

2 
I 
I 

2 
0 
2 

9 

7 

16 

Descending 

Affirmative 

Doubtful 

Negative 

I 
0 
3 

0 
2 
2 

2 
I 
I 

2 
0 
2 

I 
I 
2 

0 
0 
4 

2 
0 
2 

0 
0 

4 

8 

4 
20 

STUDIES  IN  MELODY.  27 

§13.  These  results  indicate  that  the  descending  major  third 
(4 :5)  and  the  descending  perfect  fifth  (2 :3)  exhibit  more  of  the 
quality  of  finality  than  any  of  the  other  two-tone  combinations. 
The  one  was  judged  definitely  to  end  28  times,  and  the  other 
26  times,  out  of  a  possible  32. 

The  other  intervals  showing  more  affirmative  than  negative 
judgments  are  the  ascending  perfect  fourth  (34)  with  21  affirm- 
ative judgments;  the  descending  major  second  (8:9)  with  20; 
the  ascending  minor  second  (15:16)  with  17;  and  the  ascending 
minor  sixth  (5 :8)  with  14. 

The  diminished  fifth  (45 :6^) — both  ascending  and  descending 
— and  the  descending  minor  second  (15  :i6)  each  have  the  highest 
number  of  negative  judgments — 24.  These  are  the  intervals 
that  most  clearly  lack  finality.  The  ascending  major  second  is 
next  with  21  negative  judgments,  followed  closely  by  the  ascend- 
ing and  descending  augmented  fourth,  minor  third,  minor  seventh 
and  major  seventh,  and  the  ascending  major  third.  The  per- 
centage of  negative  judgments  of  the  ascending  perfect  fifth 
and  the  descending  perfect  fourth  is  the  smallest  of  any  of  the 
intervals  judged  not  to  end. 

The  ascending  minor  seventh  (9:16)  and  the  descending  major 
seventh  (8:15)  are  both  judged  to  lack  finality,  contrary  to  the 
law  of  the  number  2,  although  their  inversions,  the  major  and 
minor  second,  conform  to  the  law.  The  ascending  minor  seventh 
has  only  7  affirmative  judgments  as  compared  with  19  negative; 
and  the  descending  major  seventh  has  8  affirmative  and  20 
negative  judgments. 

What  is  the  reason  for  the  large  number  of  negative  judgments 
on  these  larger  intervals?  One  answer  is,  that  the  tones  of  these 
wider  intervals  sometimes  failed  to  arouse  any  feeling  of  "rela- 
tionship. "  "  Those  two  tones  do  not  belong  in  the  same  melody. 
"That  second  tone  cannot  be  a  final  tone  because  it  has  no  con- 
nection whatever  with  the  first."  "No!  The  tones  aren't 
rekted."  Such  introspections  were  frequently  given  when  the 
wider  intervals  were  used.  These  not  highly  musical  observers 
experienced  a  sufficiently  strong  and  definite  feeling  of  "relation-^ 
ship"  in  the  case  of  such  a  small  interval  as  8:9,  but  found  all 
'  'relationship"  lacking  in  the  inversion  of  that  same  interval,  9:16. 


28  W.  VAN  DYKE  BINGHAM. 

This  means  that  in  formulating  the  facts  of  their  musical  expe- 
rience it  would  not  be  permissible  to  do  as  Meyer  has  done,  and 
"omit  the  number  2  as  a  factor, "  or  in  other  words  to  treat  the 
trend  and  the  "relationship"  in  any  interval  as  identical 
with  that  of  its  inversion. 

§14.  Three-fourths  of  the  24  combinations  are  judged  wo/ to 
end  more  often  than  to  end.  The  total  number  of  judgments  is 
distributed  as  follows : 


Affirmative 256  33 

Doubtful 13s  18 

Negative 377  49 

If  we  leave  out  of  consideration  the  more  complex  intervals, 
the  augmented  fourth  and  the  diminished  fifth,  the  totals  stand 
as  follows : 

PKB  CENT 

Affinnative 236  37 

Doubtful 115  18 

Negative 289  45 

From  these  facts  it  would  seem  that  in  general  it  is  somewhat 
harder  to  accept  the  second  tone  of  a  two-tone  sequence  as 
final  than  it  is  to  judge  it  to  be  lacking  in  finality. 

§15.  Do  the  results  of  these  experiments  indicate  that  de- 
scending intervals  as  such  tend  to  cause  the  feeling  of  finality? 
To  answer  this  question  the  data  of  Table  2  may  be  redistrib- 
uted so  that  the  totals  for  ascending  and  descending  intervals 
may  be  compared.  Following  are  the  totals  for  all  the  intervals 
represented  by  simple  ratios  involving  a  power  of  2,  then  for 
the  more  complex  intervals  (augmented  fourth  and  diminished 
fifth)  and  the  intervals  whose  ratios  though  simple  involve  no 
power  of  2,  and  finally  for  all  twelve  intervals  combined. 

Simple  Ratios  Involving  a  Power  of  2: 


Affirmative. 
Doubtful... 
Negative. . . 


ASCENDING 

DESCENDING 

TOTAL 

PER   CENT 

TOTAB 

PER  CENT 

89 

35 

III 

43 

49 

19 

43 

17 

118 

46 

102 

40 

STUDIES  IN  MELODY.  29 

Complex  Ratios,  and  Simple  Ratios  without  a  Power  of  2: 


Affirmative . 
Doubtful... 
Negative . . . 


ASCENDING 

DESCENDING 

TOTAL 

PER  CENT 

TOTAL 

PER  CENT 

29 

23 

27 

21 

18 

14 

25 

20 

81 

63 

76 

59 

Totals  for  all  Twelve  Intervals: 


ASCBNDINQ  DKSCKNDING 

TOTAL  PEBCBNT  TOT>L  FEB  CKNT 

Affirmative 118  31  138  36 

Doubtful 67  17  68  18 

Negative 199  52  178  46 

In  each  group,  tones  which  are  powers  of  2  had  the  position 
of  first  tone  exactly  as  many  times  as  they  had  the  position 
of  final  tone;  consequently  it  will  not  be  far  wrong  to  assume 
that  any  effects  due  to  the  operation  of  the  law  of  the  powers  of 
2  are  cancelled. 

There  is  found,  especially  in  the  first  of  these  three  sum- 
maries, some  preponderance  in  favor  of  the  descending  intervals 
as  more  definitely  final  and  of  the  ascending  intervals  as  lacking 
in  finality. 

This  effect  of  the  falling  inflection  has  been  made  the  object 
of  experimental  determination  by  Meyer.^ 

Three  tones  of  a  reed  organ  were  played  a  few  times  in  irregular  suc- 
cession, ending  on  one  of  them.  Then  they  were  played  in  a  similar  way, 
ending  on  another  one;  and  lastly,  ending  on  the  third  tone.  This  was 
repeated  until  each  subject  had  made  up  his  mind  and  written  down 
which  of  these  three  endings  was  the  most  satisfactory  to  him 

Two  classes  of  experiments  must  be  distinguished:  one  in  which  there 
was  no  tonic  effect  among  the  three  tones;  and  one  in  which  there  were 
tonic  effects.  In  the  former  case  the  three  tones  were  represented  by 
the  symbols  3,  5,  and  7;  in  the  latter,  by  2,  3,  and  9.  [The  tones  e,  g,  and 
76^  stand  in  the  ratio  of  3  :$  7 ;  c,g  and  d  would  be  represented  in  Meyer's 
sylT±)olism  by  2,  3,  and  9.]  .  .  .  .  The  three  tones  of  one  experi- 
ment were  always  within  a  single  octave.  Each  of  the  three  tones,  how- 
ever, had  an  equal  chance  of  exerting  its  influence,  i.  e.,  of  being  the 
lowest  of  the  three.    (P.  458.) 

Where  tliere  was  no  tonic  effect,  the  lower  tone,  whichever 

1  Amer.  Jour.  Psych.,  1903,  14,  456. 


30  W.  VAN  DYKE  BINGHAM. 

it  happened  to  be,  was  preferred  as  an  end  tone,  the  totals 
being  5  choices  for  the  higher,  8  for  the  middle,  and  17,  or  57 
per  cent  of  the  total,  for  the  lower  tone.  In  the  other  series, 
one  of  the  tones  was  a  'tonic'  When  this  tone  was  also  the 
lowest  tone  it  was  preferred  as  the  end-tone  in  86  per  cent  of 
the  judgments.  When  it  was  the  middle  tone  it  received 
70  per  cent  of  the  choices;  and  when  it  was  the  upper  tone 
only  7  per  cent. 

These  are  striking  results  and  one  wishes  that  these  experi- 
ments had  been  carried  farther.  Brief  as  they  are,  however, 
they  serve  to  emphasize  that  the  effect  of  finality  at  the  close 
of  a  melody  may  be  due  in  part  to  the  operation  of  other 
causes  than  the  powers  of  2  phenomenon. 

It  thus  is  obviously  desirable,  in  discussing  the  meaning  of 
our  own  results,  to  separate  as  far  as  this  is  possible  the  finality 
effect  produced  by  the  falling  inflection  from  that  which  is 
due  to  the  more  definite  pitch  relations  of  the  tones. 

§16.  We  shall  first  bring  together  the  totals  for  those 
simple  intervals  (Group  S)  whose  ratios  do  not  include  a 
pure  power  of  2,  i.  e.,  the  minor  third  (5:6)  and  the  major  sixth 
(3=5)-  The  second  summary  will  include  the  complex  inter- 
vals (Group  C)  involving  powers  of  2,  i.  e.  the  augmented 
fourth  (32:45)  and  the  diminished  fifth  (45:64).  Then  will 
come  the  eight  remaining  intervals,  all  expressible  in  simple 
ratios  one  of  whose  members  is  a  pure  power  of  2.  These  lat- 
ter it  will  be  convenient  to  separate  into  those  intervals  in 
which  the  2  tone  is  the  higher  (Group  H),  and  those  in  which 
it  is  the  lower  (Group  L). 

Group  S.     Simple  Ratios  without  a  Power  of  2 : 

INTERVAL  5  ;  (5  3  :  S  TOTAL  PEK    CENT 

Ascending 

Affirmative 7  11  18  28 

Doubtful 5  5  10  16 

Negative 20  16  36  56 

Descending 

Affirmative 10  8  18  28 

Doubtful 4  9  13  20 

Negative 18  15  33  52 


STUDIES  IN  MELODY. 


31 


Group  C.      Complex  Ratios  Involving  a  Power  of  2: 

INTERVAL         32  :  4S  4S  :  64                      total  per  cent 

Ascending 

AflSrmative 83  11  17 

Doubtful 3  5                         8  13 

Negative 21  24                       45  70 

Descending 

Affirmative 6  3                         9  14 

Doubtful 7  5                       12  19 

Negative 19  24                       43  67     . 

Simple  Ratios  Involving  a  Power  of  2: 

Group  H.  (Higher  tone  a  Power  of  2.) 

INTERVAL              15 :  16  3:4           s :  8           Q :  16  total       per  cent 
Ascending 

Affirmative 17  21            14              7  59            46 

Doubtful 4  6              6              6  22            17 

Negative ii  5            12            19  47            37 

Descending 

Affirmative 4  8              8              9  29            23 

Doubtful 4  II              8              5  28            22 

Negative 24  13            16            18  71            55 

Group  L.  (Lower  tone  a  Power  of  2.) 

INTERVAL                 8  :  16  2:3           4:6           8:9  TOTAL       per  cent 

Ascending 

Affirmative 9  lo              5              6  30            23 

Doubtful    7  8              7              5  27            21 

Negative 16  14             20            21  71             55 

Descending 

Affirmative 8  26            28            20  82            64 

Doubtful 4  3              3              5  15             12 

Negative 20  3              i              7  31            24 


According  to  the  Lipps-Meyer  formula,  intervals  of  Group 
H  should  end  better  on  the  higher  tone,  and  intervals  of 
Group  L  on  the  lower.  Consequently  in  Group  H  the  finality 
effect  due  to  the  2  ratio  is  opposed  by  the  rising-inflection 
phenomenon,  but  in  Group  L  the  two  forces  work  together. 
.  Comparing  the  totals  for  all  the  intervals  which  according 
t6  the  law  of  2  should  end,  i.  e.,  the  ascending  intervals  of 
Group  H  and  the  descending  intervals  of  Group  L,  we  find  59 
affirmative  and  47  negative  judgments  in  the  first  case,  as 
contrasted  with  82  affirmative  and  31  negative  judgments 
when  the  effects  of  the  two  forces  are  cumulative.      The 


3  2  W.  VAN  DYKE  BINGHAM. 

influence  of  the  falling  inflection  increases  the  proportion  of 
affirmative  judgments  very  noticeably.  Preference  for  the 
descending  intervals  as  more  definitely  final  does  not,  how- 
ever, come  to  light  in  comparing  the  descending  intervals  of 
Group  H  with  the  ascending  intervals  of  Group  L — intervals 
which  according  to  the  Lipps-Meyer  law  lack  finality.  In  both 
cases  the  negative  judgments  are  more  than  double  the  affirm- 
ative in  number,  and  the  totals  are  almost  exactly  the  same 
in  the  two  groups. 

It  is  instructive  to  combine  the  totals  for  the  ascending 
intervals  of  Group  H  and  the  descending  intervals  of  Group 
L,  obtaining  in  this  manner  the  totals  for  all  judgments  upon 
intervals  which  according  to  the  formula  of  Lipps  and  Meyer 
ought  to  be  judged  to  end.  These  may  be  compared  with  the 
judgments  upon  the  same  intervals  played  in  the  opposite 
direction,  which  according  to  this  law  are  characterized  by 
lack  of  finality: 

End  Tone  a  Power  of  2 : 

TOTAL  PER  CENT 

Affirmative 141  55 

Doubtful 37  14 

Negative 78  31 

First  Tone  a  Power  of  2: 

TOTAL  PER   CENT 

Affirmative 59  23 

Doubtful 55  22 

Negative 142  55 

§17.  This  last  summary  presents  strong  evidence  of  the 
operation  of  some  such  tendency  as  that  to  which  the  Lipps- 
Meyer  law  refers.  When  2  is  the  end  tone,  the  two-tone  group 
is  said  by  these  observers  to  end  in  55  per  cent  of  the  instances, 
and  not  to  end  in  31  per  cent,  the  remaining  14  per  cent  being 
'doubtful.'  When  2  is  the  first  tone  of  the  pair,  the  propor- 
tions are  reversed.  Only  23  per  cent  are  judged  to  end,  while 
55  per  cent  are  judged  to  be  lacking  in  finality. 

In  attempting  to  account  for  the  judgments  which  do  not 
conform  to  the  law,  it  is  to  be  remembered  that  in  exactly 
one  half  of  the  instances  in  each  group  the  effect  of  the  rising 


STUDIES  IN  MELODY.  33 

or  falling  inflection  was  acting  in  opposition  to  the  phenomenon 
under  discussion.  Hence  a  certain  ambiguity  and  uncertainty- 
is  sometimes  inevitable.  But  the  inadequacy  of  this  expla- 
nation to  account  for  all  of  the  facts  becomes  manifest,  when 
we  examine  afresh  the  separate  data  from  which  these  totals 
are  compiled  (p.  25).  Why  does  the  same  observer  declare  at 
one  time  that  the  ascending  minor  third,  for  instance,  ends, 
while  at  another  time  he  declares  with  no  less  positiveness 
that  it  does  not  end?  The  fact  that  some  of  the  observers 
were  but  slightly  musical  accounts  for  part  of  these  anomalies,^ 
but  some  contradictory  judgments  occur  in  all  the  records 
including  those  of  the  most  musical  observers.  How  can  the 
latter  be  explained? 

The  suggestion  was  made  that  the  fork  tones  were  so  nearly 
pure  that  the  feelings  of  "  relationship  "  were  weak  and  conse- 
quently the  reactions  produced  were  not  normal.  But  the 
real  difficulty  did  not  consist  in  any  lack  of  feelings  of  "rela- 
tionship" and  of  finality,  but  rather  in  the  fact  that  these 
feelings  were  apparently  often  misplaced.  Moreover,  control 
tests  with  harmonium  and  piano  tones  rich  in  upper  partials 
failed  to  decrease  the  proportion  of  contradictory  judgments. 

§18.  To  gather  further  data  another  series  was  arranged 
containing,  besides  the  twelve  of  the  original  series,  five 
additional  intervals:  24:25,  9:10,  27:32,  20:27  ^^^  27:40. 
Five  quite  musical  observers  served,  including  the  two  most 
musical  of  those  who  had  assisted  in  the  previous  experiment. 
The  procedure  was  varied  by  putting  the  question  differently: 
"Do  you  feel  any  desire  to  return  to  the  first  tone?" 

With  the  attention  thus  directed,  it  is  not  surprising  that 
some  of  the  observers  reported  with  certain  intervals  that 
they  desired  to  hear  the  first  tone  again,  whichever  way  the 
melodies  were  played,  ascending  or  descending.  Thus  was 
forced  into  notice  what  has  been  called  the  law  of  the  Return, 
the  law  that,  other  things  being  equal,  it  is  better  to  return  to  any 

^  For  example,  when  observer  Bl.  reported  that  an  augmented  fourth  ended  satis- 
factorily on  the  upper  tone,  he  was  asked  to  hum  the  interval  upon  which  he  had  passed 
judgment,  and  sang  a  perfect  fourth.  The  same  thing  occurred  in  the  case  of  Td, 
who,  however,  discovered  after  he  had  sung  the  interval  that  it  was  not  the  same  as  the 
one  he  had  originally  heard,  and  wanted  to  change  his  judgment  upon  it. 


34  W.  VAN  DYKE  BINGHAM. 

starting  point  whatsoever  than  not  to  return — a  simple,  funda- 
mental principle  of  musical  form,  of  art  form  of  any  kind, 
indeed. 

Another  law  to  which  the  introspections  pointed  is  not  so 
simply  formulated.  It  was  brought  to  attention  by  three 
observers  who  persistently  found  an  additional  alternative  in 
the  case  of  certain  intervals :  the  melody  lacked  finality,  there 
was  no  desire  to  return,  neither  tone  would  serve  as  an  end- 
tone  but  some  third  tone  was  demanded.  Here  was  a  melodic 
trend,  definite,  positive,  insistent;  a  property  of  a  single  pair 
of  successive  tones,  but  leading  beyond  them  to  something 
further.^ 

It  was  plain  that  the  facts  of  elementary  melodic  "rela- 
tionship" and  the  law  of  finality  of  two- tone  melodies  did 
not  tell  the  whole  story.  The  phenomenon  of  melodic  trend 
seemed  to  be  of  a  more  complex  sort,  even  in  two-tone 
groups,  than  is  implied  by  any  statement  of  a  tendency  to 
return  or  not  to  return.  Even  with  these  simple  two-tone 
sequences  it  was  necessary  to  recognize  the  operation  of  some 
such  law  as  the  following:  Two  melodically  ^'related''  tones 
tend  to  establish  a  tonality,  and  the  melody  is  judged  to  end 
only  when  the  final  tone  is  one  of  the  members  of  the  tonic 
triad — preferably  the  tonic  itself. 

This  law  is  not  asserted  to  be  a  universal  law.  Indeed  it 
is  doubtless  limited  in  its  application  to  the  experience  of 
those  reared  in  a  harmonic  musical  atmosphere.  In  so  far 
as  it  is  found  to  be  valid,  it  indicates  the  probability  that 
the  phenomena  of  melodic  trend  are  not  primary,  but  are 
derived  from  our  experience  of  consonance. 

These  experiments  were  supplemented  by  briefer  and  less 
systematic  tests  upon  a  number  of  observers,  unpracticed  in 
psychological  observation.  The  results  were  in  general  con- 
firmatory, although  not  as  strikingly  uniform  as  those  we 
have  already  given.  Mention  will  be  made  only  of  four  of 
the  observers  whose  records  are  exceptional.  Two  of  these 
exhibited  a  persistent  preference  for  endings   that  suggested 

*  These  introspections  complicated  the  records  so  much  that  it  is  not  deemed  advis- 
able to  reproduce  them  here  in  full. 


STUDIES  IN  MELODY.  35 

the  minor  mode.  Tested  upon  the  interval  of  the  minor 
third  (5 :6) — no  tonality  having  been  previously  supplied — 
these  observers  uniformly  judged  the  ending  on  the  lower 
tone,  (5),  to  be  satisfactory,  while  the  ascending  interval 
was  judged  to  be  lacking  in  finality.  One  of  these  observers 
is  a  very  musical  Welshman,  and  it  is  to  be  recalled  that 
much  of  the  characteristic  Welsh  music  is  in  the  minor  or 
as  they  call  it,  the  "la"  mode.  Tests  were  made  upon  two 
Japanese  young  men  who  had  recently  arrived  in  this  country 
and  who  professed  to  have  had  but  little  opportunity  to 
hear  European  music.  Both  were  singers  and  one  was  a 
performer  upon  the  Japanese  flute.  The  tests,  repeated, 
gave  very  conflicting  results,  and  it  became  evident  that 
either  the  interpreter  had  failed  to  make  clear  to  them  pre- 
cisely what  the  phenomenon  was  upon  which  they  were  to 
pass  judgment,  or  else  their  experience  of  melodic  trends 
differs  essentially  from  ours.  Unfortunately  it  was  not 
possible  to  carry  out  an  extensive  series  of  tests  with  these 
observers. 

§19.  For  purposes  of  comparison,  a  third  set  of  experi- 
ments was  undertaken  in  which  the  tonality  feeling  was  not 
left  to  be  contributed  by  the  hearer,  but  was  definitely  sug- 
gested to  him.  In  the  previous  experiments,  the  utmost 
pains  had  been  taken  to  exclude  the  operation  of  tonality 
by  arranging  that  neither  of  the  tones  of  a  given  group  should 
belong  to  any  tonality  which  might  have  been  suggested  by 
the  immediately  preceding  experiment.  If  any  tonality  was 
present,  it  had  a  subjective  origin.  We  have  seen  that  many 
apparently  contradictory  judgments  were  given,  as  for  instance 
when  a  minor  second  was  judged  to  end,  now  on  the  higher  and 
at  another  time  on  the  lower  tone,  both  judgments  being 
positive  and  emphatic. 

,'^In  the  experiments  now  under  discussion,  on  the  other 
hand,  the  device  was  used  of  controlling  the  tonality,  impos- 
ing it  from  without  and  testing  after  the  judgment  had  been 
made  to  see  whether  or  not  the  objectively  given  tonality  had 
been  retained.  To  facilitate  this  procedure,  a  piano  tuned 
in  equal  temperament  was  used  instead  of  the  forks. 


36  W.  VAN  DYKE  BINGHAM. 

^  These  experiments  were  carried  out  upon  five  musical 
observers,  practiced  in  psychological  observation.  Three 
of  these  were  quite  naive  as  to  the  nature  or  course  of  the 
experiment. 

All  the  intervals  of  the  tempered  scale  exclusive  of  the 
octave  were  employed.  Each  interval  was  used,  beginning 
at  every  possible  position  in  the  scale:  thus  the  ascending 
fourth  was  heard,  beginning  on  1,2,  3,  5,  6  and  7  of  the  scale. 
The  series  was  ^ven  in  double  fatigue  order.  The  experi- 
menter noted  down  the  observer's  introspections  regarding 
the  trend  of  the  interval,  or  trends,  for  several  optional 
directions  of  melodic  movement  were  often  detected.  In  these 
instances  where  more  than  one  leading  presented  itself  to 
the  observer,  an  effort  was  made  to  determine  the  relative 
strength  of  each. 

The  result  suggested  by  the  previous  experiments  came 
clearly  to  view:  so  long  as  the  given  tonality  was  maintained, 
the  trend  of  any  interval,  ascending  or  descending,  was  toward 
some  member  of  the  tonic  chord,  preferably  the  tonic  itself. 
Individual  differences  showed  themselves  as  stronger  or 
weaker  demands  for  the  tonic  as  the  end-tone,  as  over  against 
the  third  or  fifth  when  the  latter  were  nearer  than  the  tonic. 
For  example,  in  the  key  of  c,  observer  Rn  felt  that  the  sequence 
g'  f  demanded  c'  as  its  third  tone,  whereas  the  other  four 
observers  found  the  trend  to  e'  stronger.  The  uniform  ten- 
dency for  all  five  observers,  however,  with  all  the  intervals, 
was  to  rest  in  one  of  the  tones  of  the  tonic  chord. 

Our  contention  is  that  in  the  previous  experiments  with 
no  objectively  supplied  tonality,  the  anomalous  results  and 
contradictions  above  mentioned  are  explicable  on  the  hypothe- 
sis that  tonalities,  now  one  and  now  another,  arose  in  the 
mind  of  the  observer.  The  minor  second  e'-f  would  at  one  time 
chance  to  suggest  the  tonality  of  /  and  end  satisfactorily  on 
the  upper  of  the  two  tones ;  while  at  another  time  the  tonality 
of  c  would  arise,  entailing  quite  different  demands. 

§20.  We  have  too  long  neglected  to  specify  what  is  implied, 
psychologically,  in  the  term  tonality.  By  a  tonality  is 
meant  a  group  of  mutually  related  tones,  organized  about  a 


STUDIES  IN  MELODY.  3  7 

single  tone,  the  tonic,  as  the  center  of  relations.  Sub- 
jectively a  tonality  is  a  set  of  expectations,  a  group  of 
melodic  possibilities  within  which  the  course  of  the  successive 
tones  must  find  its  way,  or  suffer  the  penalty  of  not  meeting 
these  expectations  or  demands  of  the  hearer  and  so  of  being 
rejected  as  no  melody.  Of  these  different  demands,  that  for 
an  end  on  a  certain  tone  is  the  strongest  and  most  charac- 
teristic. 

It  is  not  meant  to  imply  that  this  tonality,  this  system  of  relat- 
ed pitches  with  a  common  center  of  reference,  is  present  in 
consciousness  as  a  group  of  auditory  images.  Often  there  is 
only  a  single  simple  auditory  or  vocal-motor  image  or  percept 
to  be  detected.  The  tonality  consists  in  the  attititde  of  which 
the  image  is  merely  the  superficial  manifestation  or  sensory  core. 
One  can  image  the  tone  of  320  d.v.  as  a  tonic  in  the  key  of 
e  or  as  a  median  in  the  key  of  c,  and  the  auditory  image  will 
be  identical  in  the  two  cases,  but  not  the  total  psychosis. 
There  will  be  an  entirely  different  organization  of  expectations, 
an  entirely  different  attitude,  an  entirely  different  set  of 
anticipations  and  demands,  a  preparedness  for  one  set  of 
experiences,  but  not  for  another. 

So  much  an  impartial  introspection  cannot  fail  to  disclose. 
The  position  here  advanced  is  that  these  same  "attitudes"  are 
constituted  in  large  part  of  kinaesthetic  elements — reports  of 
processes  of  motor  adjustment. 

Suggestions  toward  such  an  interpretation  of  the  tonality 
phenomenon  were  abundant  enough  from  some  of  the  ob- 
servers. When  Ha.  felt  a  melodic  trend  unrealized,  he  often 
described  it  as  a  vocal  tension,  due  to  a  tendency  to  sing  the 
desired  pitch.  An.  reported  kinaesthetic  sensations  from  the 
throat  as  accompanying  the  feeling  of  expectation.  He 
also  mentioned  sensations  of  strain  and  tension  in  other 
regions,  notably  the  diaphragm,  these  general  tensions  being 
esfJecially  prominent  at  the  instant  when  he  was  attempting 
to  retain  an  elusive  tonality  against  an  auditory  distraction 
(as  when,  for  instance,  given  the  tonality  of  c,  he  was  asked 
to  listen  to  the  interval  c-f.)  Do.  found  that  "the  effort  to 
hold  a  tonality  involves  general  organic  tensions.     Any  lapse 


38  W.  VAN  DYKE  BINGHAM. 

of  attention  or  shifting  of  muscular  tensions  precipitates  a 
shift  of  tonality.  Changes  of  breathing  will  do  this,"  etc., 
etc. 

Considerations  such  as  these  pointed  toward  the  value  of 
an  approach  to  the  problems  of  the  melody  experience  from 
the  side  of  its  motor  accompaniments,  and  resulted  in  the 
experiments  reported  in  Part  III  upon  the  motor  effects  of 
simple  melodic  stimuli. 

Whatever  the  nature  of  a  tonality  'attitude,'  whatever  its 
relations  to  sensations  of  strain  and  muscular  movement — • 
it  is  at  least  a  phenomenon  which  widely  pervades  the  musi- 
cal experience  of  hearers  who  are  familiar  with  European 
music.  The  question  now  arises  whether  either  the  tonality 
experience  or  the  experience  of  finality  in  two-tone  sequences 
is  primary,  original,  fundamental:  Does  the  law  of  2  describe 
a  primitive,  natural  tendency  or  preference,  which  has  oper- 
ated in  the  course  of  historical  development  to  mould  our 
musical  system,  or  does  it  describe  certain  secondary, 
derived  phenomena  which  would  not  be  discoverable  in  an 
experience  wholly  uninfluenced  by  association?  Proofs  of 
the  former  alternative  the  writer  has  been  unable  to  discover. 
Moreover,  the  history  of  our  musical  system  points  toward  a 
gradual  evolutionary  process  in  which  the  primary  phenomena 
of  consonance  have  been  efficacious  factors.  Hearers  whose 
minds  have  been  influenced  by  association  with  such  a  musical 
system,  when  listening  to  certain  two-tone  sequences  cannot 
avoid  feeling  a  preference  for  one  of  the  tones  as  an  end-tone. 
Some  of  these  preferences  lend  themselves  to  formulation  in 
terms  of  the  Lipps-Meyer  law  of  the  number  2;  but  this  law 
is  only  a  special  case  of  the  more  general  law  that  every 
melodic  interval  trends  toward  one  of  the  tones  of  the  tonic 
chord  of  the  tonality  which  it  arouses.  The  law  is  based 
upon  the  tendency  of  every  interval,  yes,  of  even  a  single 
musical  sound,  to  establish  a  tonality  attitude.  The  manner 
in  which  the  law  operates  will  be  evident  from  one  or  two 
simple  illustrations. 

What  shall  be  said,  for  instance,  of  those  curious,  some- 
times baffling  experiences,  in  which  a  second  tone  is  at  first 


STUDIES  IN  MELODY.  39 

unwelcome,  and  then  quickly  makes  itself  at  home  and  usurps 
the  place  of  what  had  before  been  anticipated  as  the  final 
tone?  In  certain  instances  nothing  is  more  natural  or 
inevitable.  The  first  tone  arouses  a  slight  tonality  feeling, 
making  itself  the  tonic,  so  that  if  we  call  this  tone  c,  we  shall 
have  an  'attitude'  in  which  any  of  the  tones  c,  e,  and  g  of  the 
tonic  chord  (but  especially  c  itself),  would  be  welcomed  as 
possessing  something  of  the  quality  of  finality.  Suppose  now 
we  hear  the  rising  fourth  c-f.  When  /  first  enters,  as  a  final 
tone  it  is  not  welcomed :  it  does  not  meet  the  requirements  of 
those  expectations  aroused  by  the  first  tone.  But  c-f  is  a 
harmonious  interval :  it  immediately  tends  to  shift  the  organi- 
zation of  the  tonality  feeling  to  something  which  will  include 
both  c  and  /  in  one  common  tonic  chord.  This  is,  of  course, 
the  chord /-a-c-/',  of  which/is  the  fundamental.  If  this  transi- 
tion is  successfully  made, —  and  the  chances  are  that  such  a 
transition  can  be  avoided  only  with  conscious  effort, — then 
/  becomes  a  final  tone,  and  the  interval  which  at  first  felt 
incomplete  and  unsatisfactory  comes  to  a  definite  close. 

Why  does  the  descending  fifth  end  while  the  rising  fifth 
does  not?  When  one  hears  a  tone  c  and  then  its  fifth,  both 
fit  without  readjustment  into  the  c-e-g  tonality  suggested 
by  the  first  tone,  and  for  complete  finality  one  wishes  to 
hear  again  the  tonic  c.  But  if,  instead  of  ascending  from  the 
tone  c,  we  hear  a  descending  fifth  from  the  same  starting  point 
the  situation  is  altered.  The  chord  which  includes  the 
original  c  and  this  new  tone  F  is  the  chord  F-A-c.  Our 
demand  is,  accordingly,  to  hear  as  a  final  tone  the  tonic  of 
this  chord,  which  is  F.  A  similar  treatment  applies  to 
every  instance  of  "direct  relationship"  in  which  the  law  of 
2  was  found  to  hold  good.  This  law  of  the  powers  of  2  is 
no  primitive  universal  law:  the  phenomenon  it  describes 
is^  peculiar  to  those  minds  habituated  to  a  musical  system 
whose  scale  has  a  basis  in  the  laws  of  consonance  and  dis- 
sonance. 

§21.  The  overshadowing  r61e  played  by  habit  or  association 
in  the  drama  of  our  esthetic  experience  is  not  always  recog- 
nized.    The  effect  of  habituation  in  rendering   disagreeable 


40  W.  VAN  DYKE  BINGHAM. 

sequences  tolerable  or  pleasant  and  in  changing  unrelated 
into  related  tones,  has  been  shown  by  Emerson'  and  also  by 
Meyer,  although  the  latter  finds  in  his  results  substantiation 
for  a  very  different  contention,  namely,  the  universal  applic- 
ability of  the  "complete  scale." 

Emerson  worked  with  extremely  small  melodic  intervals 
and  found  that  after  much  experience  with  these  small  inter- 
vals his  observers  developed  preferences  for  certain  sequences, 
showing  that  a  melody  can  be  constructed  of  tones  all  of 
which  are  within  the  compass  of  a  semi-tone. 

Meyer  constructed  some  'quarter-tone  melodies'  from  the 
intervals  of  his  complete  scale.  At  the  initial  performance, 
the  effect  was  judged  by  most  of  his  observers  to  be  disagree- 
able, but  on  repetition  this  judgment  was  modified,  and  two 
weeks  later,  at  still  another  hearing,  some  of  them  came  to 
appreciate  and  enjoy  the  music  which  had  before  been  strange 
and  incomprehensible.  What  an  excellent  illustration  of 
the  law  that  we  do  not  accept  as  melodically  good  that  which 
we  cannot  in  some  measure  anticipate! 

Subjected  to  careful  introspective  analysis,  the  feeling  of 
finality  attaching  to  the  second  tone  in  the  interval  3 : 4  differs 
in  no  essential  from  the  feeling  of  finality  attaching  to  the  last 
tone  of  a  purely  arbitrary  tone  combination  with  which  one 
has  grown  familiar.  In  each  instance  the  sense  of  finality  con- 
sists of  the  same  kinaesthetic  sensations  in  throat  and  dia- 
phragm, the  same  feelings  of  relaxation,  the  same  repose,  the 
same  slight  retardation  in  the  rate  of  mental  flow. 

This  effect  of  habituation  is  a  familiar  fact  in  the  musical 
experience  of  everyone.  Tonal  sequences  at  first  bizarre, 
strange,  unmusical,  later  come  to  be  appreciated,  understood 
and  enjoyed.  Some  degree  of  habituation  to  any  succession 
of  intervals  whatsoever  makes  possible  the  act  of  recognition, 
of  acknowledgment,  of  'welcoming'  the  successive  tones,  to 
use   Professor   Royce's  apt   phrase.     Habituation,   then,   is 

^L.  E.  Emerson,  "The  Feeling  Value  of  Unmusical  Tone  Intervals,"  Harvard 
Psychological  Studies.     1906,  2,  269. 

*M.  Meyer,  "Experimental  Studies  in  the  Psychology  of  Music,"  Am.  J.  Psy., 
1903,  14,  456. 


STUDIES  IN  MELODY.  4 1 

sometimes  a  powerful  factor  in  making  possible  that  active 
participation  which  seems  to  be  demanded  of  the  hearer 
before  the  succession  of  musical  sounds  can  for  him  be  unified 
into  the  organic  whole  we  call  a  melody. 

§22.  Summary.  These  studies  began  with  a  definition  of 
melody  which  laid  stress  upon  the  feeling  of  unity.  When  the 
separate  tones  of  a  series  are  felt  to  be  related  to  each  other  in 
such  a  manner  that  each  tone  forms  part  of  a  coherent  whole, 
the  succession  of  tones,  we  said,  is  felt  to  be  a  melody,  and  the 
melody  problem  was  stated  to  be  the  problem  of  explaining  how 
this  feeling  of  melodic  unity  arises.  An  analysis  of  the  psycho- 
logical elements  of  melodic  structure  revealed  many  and  varied 
sources  contributing  to  the  generation  of  this  unity.  One 
group  of  factors,  however,  stood  out  as  of  unique  importance, 
namely  those  due  to  the  relative  pitch  of  the  constituent  tones; 
and  to  the  consideration  of  problems  in  pitch  relationships  the 
scope  of  the  present  investigation  was  limited. 

A  survey  of  the  efforts  that  have  been  made  to  reduce  the 
facts  of  melodic  "relationship"  and  of  melodic  trend  to  simple 
mathematical  formulation  was  followed  by  an  account  of  three 
sets  of  experiments  upon  the  phenomena  of  melodic  trend  in 
two-tone  groups.  These  trends,  with  which  the  feelings  of 
finality  or  of  lack  of  finality  are  closely  bound  up,  were  found  to 
be  due  to  (a)  preference  for  the  lower  tone  as  such  as  an  end 
tone  (phenomenon  of  the  falling  inflection) ,  (b)  preference  for  a 
return  to  the  first  tone  as  an  end  tone,  (c)  preference  for  the 
expected  ending  (if  one  knows  that  a  given  tone  is  to  be  the 
last,  its  arrival  may  be  sufficient  to  arouse  the  feeling  of  final- 
ity quite  apart  from  the  operation  of  any  other  factors),  and, 
finally,  (d)  preference  for  an  end  on  one  of  the  tones  of  the 
tonic  chord — and  especially  the  tonic  itself — of  the  suggested 
tonality. 

This  formulation,  contrasted  with  the  formulation  in  terms 
of  'the  law  of  the  number  2,'  has  the  advantage  of  covering 
more  of  the  observed  facts'  and  the  disadvantage,  as  some  will 
consider  it,  of  conceding  that  the  phenomenon  described  is 

^  For  example,  the  numerous  instances  in  which  8  :  9  and  15  :  16  are  judged  to  end 
better  on  the  tone  which  is  not  a  power  of  2. 


42  W.  VAN  DYKE  BINGHAM. 

probably  not  elemental,  primitive,  but  rather  a  resultant, 
traceable  to  the  laws  of  habit  and  the  harmonic  structure  of 
the  music  with  which  the  observers  were  acquainted.  Accord- 
ing to  this  view,  the  laws  of  consonance  are  primary,  not  the 
laws  of  melodic  "relationship." 

This  latter  view  finds  confirmation  in  the  instances  cited 
where  the  feelings  of  "relationship"  and  of  trend  were  clearly 
the  outgrowth  of  habituation,  of  repetition,  of  custom,  of  asso- 
ciation, of  mere  expectation. 

Mention  was  made  of  the  high  importance  which  seemed  to 
attach,  in  the  introspections  of  certain  of  the  observers,  to 
kinaesthetic  factors  present  in  their  experiences  of  tonality, 
"  relationship  "  and  trend.  These  facts,  together  with  the  fact 
that  the  phenomena  of  "relationship"  are  exhibited  by  pairs 
of  tones  which  vary  so  widely  from  the  simple  ratios,  suggest 
that  it  is  not  the  sensory  but  the  motor  phase  of  the  circuit 
which  contributes  the  unity, — that  it  is  not  the  relatively  eco- 
nomical activity  of  the  sensory  nerves,  but  the  relatively  unified 
response  of  the  motor  mechanism  which  gives  rise  to  the  feeling 
of  "relationship." 

Our  problem,  then,  shapes  itself  as  the  task  of  studying  the 
motor  responses  which  melodic  stimuli  elicit,  to  discover 
whether  here  is  to  be  found  any  further  clue  to  the  explanation 
of  melodic  unity. 


PART    III 

EFFECTS    OF    MELODIC    STIMULI   UPON    MUSCULAR  MOVEMENT 

§23  To  gather  definite  data  regarding  the  relation  of 
movement  to  the  melody  experience,  the  following  experi- 
ments were  undertaken,  designed  to  test  the  effects  of  simple 
melodic  stimuli  upon  on-going  motor  processes,  voluntary  and 
involuntary. 

The  voluntary  process  studied  was  the  tapping  movement 
of  the  index  finger  of  the  right  hand.  This  movement  was 
chosen  because  of  its  simplicity  and  naturalness,  and  because 
after  a  little  practice  it  tends  toward  automatism,  leaving  the 
attention  free  to  be  focussed  upon  the  stimulus.  Such  devices 
as  the  Jastrow  automatograph  and  the  Delabarre  muscle- 
recorder  were  rejected  in  favor  of  the  means  here  described, 
because  it  seemed  highly  probable  that  changes  in  innerva- 
tion would  become  most  readily  manifest  as  alterations  of  a 
motor  process  already  going  forward.  Other  factors  remain- 
ing constant,  it  is  to  be  expected  that  a  neural  current  will 
tend,  at  least  in  part,  to  find  its  way  out  of  the  central  system 
along  that  motor  channel  which  is  already  in  use.  Moreover 
the  investigations  of  Stetson^  and  others  upon  complex  or 
"combined"  rhythms  have  made  it  certain  that  a  concurrent 
movement  coming  into  coordination  will  affect  an  accom- 
panying uniform  movement. 

The  form  of  apparatus  used  is  an  adaptation  of  the  simple 
device  employed  by  Stetson  for  recording  rhythmical  move- 
ments. The  hand  and  forearm  rested  naturally  upon  the 
arm-rest  leaving  the  index  finger  free  to  move  throughout 
its  entire  range  of  flexion  and  extension  without  contact. 
(Sefe  accompanying  figure).  This  free,  unrestricted  move- 
ment was  chosen  because  it  was  found  that  when  the  finger 
taps  against  a  hard  surface  the  contact  sensations  serve  as  a 

1  R.  H.  Stetson:  "A  Motor  Theory  of  Rhythm  and  Discrete  Succession."  Psych. 
Rev.  1905, 12,  250. 


44 


W.  VAN  DYKE  BINGHAM. 


sensory  control  which  regulates  and  steadies  the  movement. 
As  our  purpose  was  to  detect  any  slight  variations  which 
the  melodic  stimuli  might  produce  in  this  motor  process,  it 
was  obviously  better  to  avoid  as  many .  of  these  controls  as 
possible. 

The  periodic  movement  of  the  finger  was  recorded  in  all 
its  details  as  far  as  changes  in  rate,  form,  and  amplitude 
of  movement  in  a  vertical  direction  are  concerned,  by  means 
of  the  recording  device  above  mentioned.  From  the  leather 
finger-cot  a  silk  thread  ran  over  a  tiny  pulley  and  through 


Figure  No.  i 

glass  guides  which  prevented  any  loose  motion.  This  thread 
led  to  a  rubber  thread,  in  the  middle  of  which  was  an  alumi- 
num writing  point,  which  traced  a  record  of  the  finger  move- 
ment upon  the  belt  of  smoked  paper.  A  slight  torsion  of 
the  rubber  served  to  keep  the  writing  point  against  the  sur- 
face of  the  kymographic  belt.  By  varying  the  length  of  the 
rubber  on  either  side  of  the  writing  point  the  relative  ampli- 
tude of  the  curve  could  be  made  as  small  as  desired.  Most 
of  the  records,  however,  were  taken  with  all  of  the  rubber 
upon  one  side  of  the  writing  point  so  that  the  curve  was 
equal  not  only  in  form  but  also  in  amplitude  to  the  vertical 


STUDIES  IN  MELODY. 


45 


component  of  the  finger  movement.  The  tension  of  this 
delicate  rubber  was  so  sHght  that  it  was  barely  perceptible 
to  the  observer,  and  did  not  interfere  with  the  freedom  and 
naturalness  of  the  movement.  Indeed,  the  superiority  of 
this  recording  device  over  that  of  a  tambour  lever  lies  in  the 
perfect  freedom  of  lateral  motion  allowed;  because  there  is 
no  restraint  upon  the  finger  movement,  there  are  no  sensory 
controls  other  than  those  cutaneous  and  kinaesthetic  sensa- 
tions due  to  the  movement  itself. 

The  belt  of  smoked  paper  ran  between  two  cylinders  placed 
about  two  meters  apart.  It  was  driven  by  an  alternating 
current,  constant-speed  motor  whose  only  variations  were  due 
to  fluctuations  in  the  rate  of  the  generator  of  the  Cambridge 
lighting  plant.  Tests  with  vibrating  forks  of  50  d.  v.  and 
500  d.  V.  showed  that  the  maximum  variations  in  the  rate 
of  the  belt  of  smoked  paper  were  less  than  one  and  one-half  per 
cent.  As  a  precautionary  measure,  however,  a  time  line 
was  made  a  feature  of  all  the  records,  interruptions  at  periods 
of  one  second  being  furnished  by  means  of  a  Lough  self- 
actuating  pendulum,  placed  in  a  distant  room.^  Precaution 
was  taken  to  banish  all  sound  which  might  arise  from  the 
recording  apparatus,  such  as  the  ticking  of  the  electric 
markers.  The  driving  mechanism  was  placed  outside  of  the 
experimenting  room,  as  otherwise  a  low  hum  from  the  motor 
could  be  heard  even  when  it  was  encased  in  a  "sound-proof" 
box. 

One  electric  marker,  as  has  been  said,  furnished  the  time  line. 
This  line  also  served  as  base  line  for  measuring  amplitudes. 
Another  marker  was  in  circuit  with  the  keyboard  of  the  har- 
monium which  was  used  for  giving  the  melodic  stimuli,  and 
furnished  the  record  of  the  course  of  the  experiment.^  A 
silent  pendulum  was  used  to  aid  the  experimenter  in  con- 
trolling the  length  of  the  sounds.     The  smoked  record  was 

^  Only  alternate  taps  of  the  time-marker,  i.  e.,  one  every  two  seconds,  are  visible 
in  the  sample  records  reproduced  on  p.  51. 

^  It  is  the  opinion  of  the  experimenter  that  a  simple  pneumatic  attachment  to  the 
keyboard  of  an  organ  or  piano  with  tambour  recorder  would  on  the  whole  prove  more 
satisfactory  than  an  electrical  attachment. 


46  W.  VAN  DYKE  BINGHAM. 

made  permanent  by  being  sprayed  with  a  ten  per  cent  solu- 
tion of  gum  sandarac  in  alcohol.^ 

Pneumographs  of  the  Sumner  pattern  were  employed  to 
record  the  abdominal  and  thoracic  breathing.  The  degree 
of  sensitivity  of  pneumographs  and  tambours  is  shown  by  the 
clearness  with  which  the  pulse-beat  appears  on  the  pneumo- 
graphic  tracings,  quite  plainly  enough  indeed,  especially  on  the 
curve  of  the  abdominal  breathing,  to  permit  the  computation 
of  the  pulse  rate  if  desired. 

Nothing  of  significance  for  the  present  investigation  ap- 
peared, however,  in  these  pneumographic  curves.  The  reason 
doubtless  is  found  not  in  the  fact  that  melodic  stimuli  do 
not  produce  important  modifications  in  the  breathing,  but 
rather  in  the  fact  that  the  duration  of  the  stimulus  used  was 
too  brief  to  permit  the  characteristic  alterations  to  appear. 
In  this  respect  the  conditions  were  quite  the  reverse  of  those  in 
the  experiments  of  Foster  and  Gamble.^  These  experimenters 
using  musical  selections  of  various  kinds  as  stimuli  found  that 
listening  always  tends  to  shorten  the  expiratory  pause  and  to 
make  the  breathing  faster  and  shallower,  but  not  steadier;  but 
no  remarkable  differences  were  found  in  the  effects  of  loud  and 
soft  or  major  and  minor  music.  One  is  not  surprised  to  learn 
that  characteristic  breathing  phenomena  could  not  be  isolated 
when  use  was  made  of  such  highly  complex  stimuli  as  actual 
musical  selections. 

§24  When  the  subject  had  taken  his  place  and  the  pneu- 
mographs and  finger  apparatus  had  been  adjusted,  the  nature 
of  the  particular  experiment  to  be  performed  was  explained. 
The  number  of  tones  which  were  to  be  used  was  told,  but 
nothing  further  was  said  regarding  the  nature  of  the  melodic 
intervals.  The  subject  then  closed  his  eyes  and  the  experi- 
menter started  the  kymograph,  so  that  a  brief  record  of  the 
breathing  was  obtained   before  the  finger  movement  began. 

^  The  double-glazed  paper  used  was  too  thick  to  be  fixed  by  the  usual  device  of 
painting  on  the  wrong  side.  The  use  of  a  spray  proved  to  be  convenient  and  expedi- 
tious. A  "  fixative  spray, "  to  be  had  for  ten  cents  at  any  art  store,  when  fitted  to  a  foot- 
power  bellows,  proves  very  satisfactory. 

^Eugenia  Foster  and  E.  A.  McC.  Gamble:    "The  Effect  of  Music  on  Thoracic 
Breathing."    Amer.  Jour.  Psych.,  1906.  77,  406. 


STUDIES  IN  MELODY. 


47 


At  a  word  from  the  experimenter  the  subject  began  the  tap- 
ping movement  taking  whatever  rate  was  most  natural  to 
him.  After  the  tapping  had  continued  for  twelve  seconds  or 
longer  the  melodic  stimulus  was  given.  The  tones  were 
played  upon  a  reed  organ  the  mechanism  of  which  was  in 
electrical  connection  with  a  marker  which  recorded  the  instant 
of  depressing  and  raising  the  keys.  The  general  plan  was  for 
the  experimenter  to  sound  each  tone  for  a  period  of  three 
seconds.  It  may  be  thought  that  this  period  was  unneces- 
sarily long,  but  the  observers  did  not  find  it  objectionable 
and  it  has  two  very  obvious  advantages.  In  the  first  place 
a  period  as  long  as  three  seconds  is  sufficient  to  permit  any 
motor  changes  which  the  stimulus  may  produce  to  become 
evident  in  the  record  of  the  finger  movement.  And  in  the 
second  place  the  use  of  the  three-second  period  minimized, 
if  it  did  not  indeed  entirely  rule  out,  the  factor  of  rhythm. 
Stimuli  whose  rate  is  as  slow  as  one  in  three  seconds  do  not 
tend  to  become  rhythmized. 

After  the  melodic  stimulus  the  tapping  was  continued  for 
ten  seconds  or  longer.  The  observer  was  then  called  upon  to 
give  his  introspection.  Aside  from  a  general  introspective 
record  of  the  course  of  the  experiment,  the  naturalness  of 
the  tapping,  effect  of  external  disturbances,  and  the  like,  the 
points  toward  which  inquiry  was  especially  directed  were 
two:  first,  does  this  melody  end?  Has  it  the  characteristic 
of  finality,  or  is  it  unfinished?  Does  it  leave  you  in  suspense? 
Does  it  demand  something  further?  Secondly,  the  question 
was  raised  as  to  whether  or  not  the  melody  was  pleasing.  In 
many  cases  but  not  in  all,  these  two  aspects,  the  affective  and 
the  aspect  of  completeness,  seemed  to  be  felt  as  identical ;  that 
is  to  say,  a  melody  was  judged  to  be  agreeable  because  it 
came  to  a  good  ending,  or  to  be  unsatisfactory  because 
incomplete.  Not  infrequently,  however,  one  met  with  intro- 
spective reports  like  the  following:  "That  is  good;  I  like  that 
but  it  is  not  finished,"  or,  "  That  isn't  particularly  pleasant, 
but  it  ends  very  emphatically." 

A  word  ought  to  be  said  about  the  way  in  which  the  observers 
were  first  brought  to  an  understanding  of  the  phenomenon 


48  W.  VAN  DYKE  BINGHAM. 

which  was  under  investigation.  They  were  not  told  what 
the  phenomenon  was,  and  then  asked  if  they  could  observe  it. 
On  the  contrary,  the  plan  employed  was  to  play  an  inter- 
val of  an  ascending  fifth  and  then  to  play  the  same  interval 
descending  and  then  ask  for  a  full  introspective  account. 
Some  observers  would  quickly  detect  the  feeling  of 
relaxation,  of  repose,  of  completeness  which  accompanied  the 
perceptiom  of  the  descending  fifth  and  which  was  lacking 
when  the  ascending  fifth  was  heard.  Lest  they  should 
immediately  form  the  opinion  that  this  characteristic  of 
finality  always  accompanied  a  descending  interval,  the  per- 
fect fourth  was  next  played.  This  interval  they  soon  dis- 
covered makes  a  better  ending  upon  the  upper  tone  than  upon 
the  lower.  Only  after  the  observers  had  become  thoroughly 
familiar  with  the  phenomenon  were  they  asked  to  serve  as 
reagents  in  the  main  experiments.  With  two  of  the  obser- 
vers not  a  little  persistence  together  with  many  repetitions 
of  the  intervals  was  required  before  they  discovered  the 
phenomenon,  but  in  every  case  it  was  a  genuine  discovery 
of  their  own,  and  was  not  suggested  to  them. 

§25  The  observers  were  research  students  or  instructors 
in  the  Harvard  Psychological  Laboratory,  with  the  excep- 
tion of  Po.,  who  had,  however,  had  training  as  an  observer 
elsewhere.     All  with  the  exception  of  Da,  and  Pu.  were  men. 

It  will  be  convenient  to  divide  the  observers  into  three 
groups  according  to  musical  ability.  This  classification  is 
based  upon  tests  in  recognition  and  vocal  reproduction  of 
melodic  intervals,  immediate  memory  for  intervals  and  for 
short  melodies,  and  recognition  of  the  fundamental  note  of  a 
chord.'  The  method  employed  in  this  last  test  was  as  fol- 
lows: a  three-clang  chord  was  played,  and  after  it  a  single 
low  clang,  with  the  question,  "Is  this  the  fundamental  basic 
tone  of  this  chord?  Does  it,  in  a  way,  represent  the  whole 
chord?  If  you  had  to  supply  a  bass  to  this  chord,  is  this 
the  tone  you  would  use?"  Twenty  four  chords  were  given, 
eight  in   the  first  position,  and  eight  each  in  the  first  and 

1  The  writer  acknowledges  indebtedness  to  Professor  Meyer  for  the  suggestion  o  f 
this  test  of  musical  ability. 


STUDIES  IN  MELODY. 


49 


second  inversions.  The  low  tone  which  followed  was  always 
a  lower  octave  of  one  of  the  tones  of  the  chord,  and  in  one 
half  of  the  instances  it  was  the  fundamental.  The  number 
of  right  judgments  for  each  observer  is  given  in  the  second 
column  of  the  accompanying  Table  3.     The  percentages  in 

TABLE  NO.   3 
Tests  of  musical  ability. 


RECOGNITION   OP   FUNDAMENTAL  OF   CHORD 

VOCAL  REPRODUCTION  OF  FUNDAMENTAL  TONE 

E 

1 
0 

i 

s 

3 
S 

1 

1 

a 
8 

•1 

f 

3 
2 

g 

Po 

Rk 

Rg 

Da 

Ho 

Fr 

Ta 

Mc 

Pu 

24 
24 

22 
20 
20 
16 
12 

8 
4 

0 
0 
2 
2 
2 

4 
8 

5 
0 

0 
0 
0 
2 
2 
4 

4 
II 
20 

100 
100 
92 
88 
88 
75 
S8 
56 
S8 

24 
23 

22 
23 
17 
18 
12 
10 

0 

I 
2 

1 

5 
5 

12 
10 

0 
0 
0 
0 
2 
I 
0 
4 

100 

97 
92 

97 
75 
77 
50 
50 

(In  computing  percentages,  doubtful  cases  are  distributed  equally  between  right  and  wrong  cases.) 


the  last  column  represent  the  success  of  the  subjects  in  hum- 
ming the  fundamental  tone  after  hearing  the  chord,  the 
series  of  chords  used  being  similar  to  the  one  employed  in 
the  previous  test.  Errors  were  most  frequently  made  when 
the  low  note  was  not  the  fundamental,  but  was  a  lower 
octave  of  the  highest  note  in  the  chord.  It  was  found  after 
the  series  was  ended  that  fewer  errors  of  this  kind  are  made 
if  the  observer  is  instructed  not  to  give  his  judgment  immedi- 
ately, but  first  to  image  the  three  tones  of  the  chord  separately, 
choose  the  fundamental,  and  then  make  the  comparison  with 
the'  low  tone.  On  repetition  of  the  test,  this  precaution 
served  to  eliminate  all  errors  from  the  judgments  of  Rk.. 
Ho.,  and  Da.,  but  did  not  operate  so  successfully  with  those 
observers  whose  auditory  imagination  is  less  facile. 

The  results  of  these  tests  when  combined  with  the  other 


50  W.  VAN  DYKE  BINGHAM. 

observations  on  musical  ability  and  with  the  results  of  an 
inquiry  into  the  observers'  musical  interests,  their  early 
training  and  later  musical  experience,  made  it  evident  that 
the  first  three  observers  on  the  list  had  a  fair  order  of  musical 
capacity,  although  Po.  was  the  only  one  whose  abilities  had 
been  much  developed  by  training.  The  last  three  observers 
form  a  distinct  group,  since  they  all  fall  much  below  the 
others  in  the  tests  reported  in  Table  3,  and  also  in  accuracy 
of  recognition  and  reproduction  of  melodic  intervals.  Pu. 
could  not  even  be  induced  to  attempt  vocal  reproduction. 
The  remaining  three  observers  form  an  intermediate  group. 
None  of  the  nine  were  entirely  lacking  in  musical  interest, 
although  the  range  represented  was  a  very  wide  one. 
An  accurate  test  of  ability  in  pitch  discrimination  was 
not  carried  through  to  completion  because  it  became  evident 
that  accuracy  in  the  discrimination  of  small  differences  of 
pitch  is  no  indication  of  musical  ability.  Po.  and  Rg.  did 
not  serve  during  the  preliminary  experiments.  Da.  and  Mc. 
did  not  serve  during  the  second  half  year,  and  their  records 
are  included  only  in  the  first  of  the  tables  presented  here. 
Each  observer  served  for  a  period  of  three  quarters  of  an  hour 
once  a  week. 

The  observers  it  will  be  recalled  were  directed  to  take 
whatever  rate  of  finger  movement  seemed  most  natural  to 
them.  The  individual  differences,  and  also  the  individual 
variations  from  time  to  time,  proved  to  be  extremely  wide. 
Early  in  the  practice  experiments,  the  tapping  of  Rk.,  Da., 
Ta.,  and  Mc.  was  much  slower  than  it  became  later  on,  and 
nearly  all  of  the  observers  showed  some  tendency  to  increase 
the  natural  rate  with  practice.  Within  a  series  of  experi- 
ments at  a  single  sitting,  Rg.,  Rk.,  and  Mc.  were  apt  to 
choose  a  much  more  rapid  rate  for  the  later  experiments, 
unless  they  happened  to  select  an  unusually  rapid  rate  to 
begin  with.  This  they  were  apt  to  do  if  they  had  been  walk- 
ing rapidly  or  otherwise  exercising  shortly  before,  or  if  they 
had  been  under  any  slight  excitement. 

Not  only  do  the  records  show  great  individual  differences 
in  the  rate  of  finger  movement,  but  also  in  the  amplitude  and 


3 


a>  d 
boa> 

SB 

*^  > 
o 


i «  S  g  I 


5  2  W.  VAN  DYKE  BINGHAM. 

the  general  form.  Ta.'s  record  is  characteristically  slow, 
wide,  and  extremely  regular.  The  back  stroke  is  similar  to 
the  beat  stroke  in  every  respect,  and  the  transitions  from  the 
ballistic  part  of  the  movement  to  the  controlled  portion  are 
smooth  and  even.  The  tapping  of  Da.  and  Mc.  is  also  slow 
and  wide,  but  very  different  from  that  of  Ta.  because  the 
ballistic  strokes  are  made  with  a  jerky  movement,  and  the 
portions  of  the  curve  between  the  ballistic  strokes  are  very 
irregular.  The  muscular  coordination  is  much  less  accurate. 
Ho.  and  Pu.  also  use  a  characteristically  slow  rate,  but  the 
amplitude  of  movement  is  small.  One  finds  very  consider- 
able variations  in  amplitude  in  the  records  of  both  these 
observers.  There  is  also  an  irregularity  of  line  due  to  the 
fact  that  the  ballistic  portion  of  the  movement  seems  to  be 
almost  wholly  lacking,  even  from  the  beat  strokes,  {i.  e.,  the 
finger  seems  to  be  almost  continuously  under  control  of 
extensor  and  flexor  muscle  sets  combined.)  The  maximum 
velocity  of  the  beat  stroke  is  much  less  with  these  observers 
than  with  any  of  the  others.  Rk.  and  Rg.  are  the  two  who 
show  the  widest  variations  of  natural  rate  from  time  to  time 
and  also  the  greatest  changes  in  the  form  of  the  finger  move- 
ment. Both  of  them  use  a  medium  amplitude,  but  this  ampli- 
tude varies  widely.  On  the  whole,  their  records  show  that  a 
much  greater  prominence  is  given  to  the  ballistic  phase  in 
both  beat  stroke  and  back  stroke.  In  Po.'s  records,  which 
exhibit  the  most  rapid  rates  of  any  of  the  observers,  there 
is  very  little  in  the  curve  other  than  the  ballistic  phase :  there 
is  almost  no  pause  between  strokes.  In  the  records  of  Fr., 
on  the  other  hand,  there  is  always  between  the  vigorous 
ballistic  strokes  a  relatively  long  relaxation  phase  during 
which  the  movement  is  extremely  irregular:  during  these 
periods  the  finger  seems  to  be  not  under  the  control  of  either 
the  extensors  or  the  flexors. 

With  reference  to  the  amplitude  of  finger  movement,  it 
may  be  noted  that  with  the  exception  of  Ta.,  those  who  used 
a  wide  amplitude  were  those  who  had  had  some  practice  at 
the  piano. 


STUDIES  IN  MELODY. 
TABLE  NO.  4 


53 


Normal  record  of  rate  of  finger  movement,  and  fatigue  record.  Rate  of  tapping  during  suc- 
cessive periods  of  three  seconds  each.  Read  from  left  to  right.  The  slowest  rates  are 
printed  in  bold  faced  type.     Fastest  rates  in  italics. 


m 

> 
« 

H 

a 

n 
o 

NOBUAL  BKCOBD 

FATIOUB  BBCOBD 

Po 

Rg 

Rk  ... 
Da  ... 
Ho  ... 

Fr 

Ta  . . . . 
Mc... 
Pu 

107 

97 

96 

208 

78 

84 

112 

256 

104 

133 

1^5 

93 

208 

78 

85 

102 

256 
106 
133 

lOI 

90 

206 

76 

83 
104 

252 
99 

130 

105 
91 

208 

77 

86 

107 

254 

lOI 

133 

loS 
90 

207 
78 
87 

104 

249 

99 
132 
100 

91 

210 

80 

82 

104 

252 
92 

131 
103 

92 

220 

79 

88 

109 

260 

lOO 

126 

105 

94 

217 

79 

85 

no 

263 
99 

130 

104 
89 

214 
81 
86 

113 

m 
Hi 

3  OS  « 
He's 

Ill 

232 

106 
124 

99 
86 

221 
77 
93 

114 

239 

104 
124 

97 
88 

225 
77 
91 

118 

23s 

108 

121 

98 

88 

224 

78 

96 

"5 

§26  In  the  accompanying  Table  4  are  given  the  measure- 
ments of  a  set  of  records  taken  without  distraction  or  stimulus 
of  any  kind,  for  purposes  of  comparison  with  records  in 
which  melodic  stimuli  were  used.  Each  number  gives  the 
rate  of  finger  movement  during  a  period  of  three  seconds. 
The  rate  is  expressed  in  beats  per  minute,  which  is  the  same 
as  the  method  employed  in  music  for  designating  rates.  The 
numbers,  then,  represent  the  metronome  rates  at  which  the 
observer  was  tapping  during  successive  periods  of  three 
seconds  each.  To  facilitate  the  reading  of  the  table,  the 
rate  of  the  period  of  slowest  tapping  within  the  record  of 
each  observer  is  printed  in  bold-faced  type,  and  the  fastest 
rate  is  printed  in  italics.  A  glance  at  the  table  will  show  the 
extremes  between  which  the  rate  of  tapping  varied  within  the 
course  of  the  period  of  twenty-seven  seconds  covered  by  the 
record.  It  will  be  seen  that  four  of  the  nine  observers 
exhibit  a  tendency  toward  an  increase  in  rate  during  this 
time,  while  an  opposite  tendency  appears  in  the  records  of 
two  observers. 

The  question  naturally  arises  whether  the  factor  of  fatigue 
may  not  enter  in  to  modify  the  nature  of  the  tapping  move- 
ment as  the  experiment  proceeds.  This  does  not  seem  to  be 
the  case  when  an  experiment  does  not  continue  for  more 


54  W.  VAN  DYKE  BINGHAM. 

than  thirty  seconds,  as  was  the  case  with  nearly  all  of  those 
to  be  described  below.  For  purposes  of  comparison,  how- 
ever, there  is  given  in  connection  with  the  normal  record  of 
the  accompanying  table  what  may  be  called  a  fatigue  record. 
This  is  really  a  continuation  of  the  normal  records,  one 
minute  of  unrecorded  tapping  having  been  permitted  to  elapse 
between  the  close  of  the  normal  record  and  the  beginning  of  the 
fatigue  record.  During  this  interval  the  rate  of  tapping  of 
four  of  the  observers  showed  a  diminution.  With  four  of  the 
others  an  increase  in  rate  is  seen.  The  record  of  Fr.  showed 
the  greatest  variability  and  irregularity  during  this  closing 
period.  Only  two  observers.  Da.  and  Mc,  reported  any 
feeling  of  fatigue  after  this  experiment. 

Fatigue  makes  its  appearance  very  quickly  if  a  rate  more 
rapid  than  the  natural  rate  of  tapping  is  employed.  When 
the  reagent  taps  as  rapidly  as  possible  the  entrance  of  fatigue 
brings  with  it  a  slowing  of  the  rate  and  an  increase  in  irregu- 
larity of  rate  and  of  amplitude. 

§27  Tables  5  and  6  exhibit  the  effect  of  auditory  stimuli 
upon  the  rate  of  tapping.  These  tables  are  prepared  in  a 
manner  similar  to  the  table  of  normal  tapping;  each  number 
represents  the  rate  of  tapping  during  a  three-second  period. 
Measurements  of  the  first  few  taps  of  each  record  were  not 
made  because  they  are  certain  to  be  more  or  less  irregular. 
Measurements  of  the  rate  of  tapping  are  given  for  three  periods 
of  three  seconds  each  before  the  incoming  of  the  stimulus. 
The  stimulus  consisted  of  the  tone  a  sounded  for  six  seconds 
on  the  harmonium.  Then  after  an  interval  of  three  seconds, 
this  tone  was  sounded  again,  this  time  for  only  three  seconds, 
but  it  was  immediately  repeated  and  sustained  for  three 
seconds  longer. 

A  study  of  this  table  should  disclose  the  effects  which  are 
produced  upon  the  rate  of  tapping  by  a  musical  sound  and  also 
by  the  repetition  of  a  musical  sound.  It  will  be  noticed  that 
in  the  records  of  four  of  the  seven  observers  there  is  a  marked 
diminution  of  rate  following  the  entrance  of  the  first  stimulus. 
The  record  of  one  observer  shows  a  marked  increase  of  rate 
at  this  point.     In  all  cases  there  appears  to  be  a  tendency 


STUDIES  IN  MELODY. 
TABLE  NO.  5 


55 


Effect  of  a  single  tone,  and  of  that  tone  repeated,  on  rate  of  finger-movement.  The  rate  during 
each  three-second  period  of  the  experiment  is  given.  Read  from  left  to  right.  Numbers 
showing  decrease  in  rate  at  critical  points  in  the  record  are  printed  in  bold  face  type; 
increases  in  rate  are  printed  in  italics. 


a 

a 

a 

(6  SEC) 

(3  SBC) 

(3  SEC) 

136 

140 

141 

123 

130 

132 

132 

135 

132 

lOI 

109 

104 

82 

96 

80 

78 

73 

(97)* 

79 

81 

80 

79 

78 

76 

72 

72 

71 

159 

157 

157 

166 

15s 

163 

160 

151 

150 

122 

116 

118 

128 

125 

118 

121 

127 

129 

77 

77 

76 

69 

75 

77 

76 

76 

77 

60 

62 

69 

66 

65 

65 

66 

67 

72 

Rk. 
Da. 
Ho. 
Fr.. 
Mc. 
Ta. 
Pu. 


138 
90 
69 
152 
130 
80 
72 


•Stopped  tapping  for  1.2  sec.  when  tone  stopped;  and  then  began  at  rate  of  97. 


TABLE  NO.    6 


Effect  of  sudden  noise  on  rate  of  finger-movement, 
fifth  three-second  period  of  the  record. 


Entrance  of  stimulus  at  beginning  of 


Po 
Rk 
Ho 
Fr. 
Ta 


216 

216 

214 

218 

226 

216 

214 

210 

150 

154 

153 

152 

152 

153 

160 

159 

116 

116 

114 

"3 

104 

119 

114 

116 

202 

187 

185 

190 

ig8 

194 

194 

197 

69 

72 

71 

72 

67 

69 

70 

70 

to  return  to  the  original  rate  while  the  tone  is  still  sounding. 
The  records  of  three  observers  show  another  diminution  in 
rate  immediately  following  the  cessation  of  the  stimulus,  but 
no  decided  change  occurs  in  the  other  four  records  at  this 
point.  With  the  entrance  of  the  stimulus  the  second  time  a 
retardation  occurs  in  three  records,  but  this  time  it  is  not 
nearly  as  large  as  in  the  first  instance.  The  repetition  of  this 
stimulus  is  accompanied  by  an  increase  in  the  rate  of  one 
observer  and  a  decrease  in  the  rate  of  another,  the  rates  of 
tlie  other  five  observers  not  changing  materially  at  this  point 
in  the  records.  The  cessation  of  the  stimulus,  however,  is 
accompanied  by  an  increase  in  the  rate  with  two  observers, 
and  a  decrease  in  a  single  instance.  One  observer  stopped 
tapping  entirely  for  a  brief  time  when  the  stimulus  stopped 
and  then  began  again  at  a  rapid  rate. 


56  W.  VAN  DYKE  BINGHAM. 

It  thus  becomes  evident  that  under  the  conditions  of  this 
experiment  the  entrance  of  an  auditory-  stimulus  introduces 
a  disturbance  in  the  process  of  tapping  which  shows  itself  as 
a  change  in  rate,  usually  of  the  nature  of  a  retardation. 
The  nature  of  the  disturbance  to  the  tapping  is  made  very 
evident  by  direct  inspection  of  the  kymographic  records. 
The  next  tap  after  the  one  during  which  the  stimulus  enters 
is  frequently  the  slowest  and  also  has  the  greatest  amplitude 
of  excursion  of  any  tap  on  the  record.  The  entrance  of  the 
stimulus  a  second  time,  after  a  pause,  produces  similar  but 
much  less  marked  effects;  and  when  no  time  interval  elapses 
between  the  clang  stimulus  and  its  repetition  no  effect  what- 
ever is  apparent. 

The  effects  of  a  momentary  noise  as  a  distraction  are  illus- 
trated in  the  experiments  summarized  in  Table  6.  Here, 
too,  a  marked  change  of  rate  appears  in  nearly  every  instance. 
The  solitary  exception  is  Rk.,  and  a  closer  examination  of  his 
record  than  the  table  permits  shows  clearly  that  here  too  the 
the  stimulus  had  its  effect.  The  tap  immediately  following 
the  one  in  which  the  stimulus  entered  is  the  slowest  tap  of 
the  record,  but  in  this  instance  it  is  followed  immediately  by 
taps  of  a  more  rapid  rate  which  bring  the  rate  for  the  entire 
three  seconds  up  to  the  figure  given. 

It  seems  to  be  a  general  tendency,  then,  for  alterations  in  the 
natural  tapping  rate  of  the  finger  to  occur  upon  the  entrance 
into  consciousness  of  an  auditory  sensation.  This  very 
natural  phenomenon  does  not  call  for  an  elaborate  explana- 
tion. It  may  be  dismissed  by  referring  it  to  that  large  group 
of  experiences  which  have  as  their  most  prominent  feature  the 
characteristic  of  "shock,"  of  sudden  disturbance  of  equi- 
librium demanding  an  adjusting  act  of  attention,  and  which 
consequently  interfere  more  or  less  with  pre-existing  adjust- 
ments and  on-going  activities.  Stated  in  strictly  neural 
terms,  the  phenomenon  is  reducible  to  an  instance  of  the 
general  law  of  diffusion,  the  auditory  stimulus  introducing 
a  shift  of  neural  tensions  throughout  the  cortex,  and  more 
particularly  affecting  those  localities  in  the  Rolandic  region 
which  are  active  at  the  time. 


STUDIES  IN  MELODY.  S  7 

The  modification  of  rate  shows  itself  most  frequently  as  a 
retardation  probably  because  new  activities  of  adjustment 
result  in  inhibition  of  the  finger  movement  through  drainage 
of  the  neural  energies  elsewhere.  To  explain  those  relatively 
infrequent  instances  (15  per  cent  of  the  total  number)  where 
acceleration  follows  the  entrance  of  the  auditory  stimulus, 
one  might  assume  that  the  stimulus  operates  to  produce  a 
greater  alertness,  or  heightened  general  activity  in  which  the 
tapping  movement  shares.  To  explain  why  the  very  first  tap 
following  the  onset  of  the  stimulus  is  sometimes  unusually 
wide  and  of  long  duration,  but  occasionally  the  reverse, 
recourse  may  be  had  to  the  facts  brought  out  by  Hofbauer^ 
and  Cleghom^  that  an  auditory  stimulus  occurring  at  the 
beginning  of  the  contraction  phase  of  a  movement  augments 
the  movement  and  this  reinforcement  makes  the  total  duration 
of  the  contraction-relaxation  process  greater;  but  if  the 
stimulus  enters  at  the  beginning  of  the  relaxation  phase  of  the 
cycle,  the  process  of  relaxation  is  hastened  and  the  total  period 
is  diminished. 

§28  We  may  now  turn  to  the  experiments  in  which  melo- 
dic stimuli  were  employed,  asking  what  significant  changes  of 
rate  appear,  to  what  extent  these  variations  are  the  same  for 
the  different  observers  under  identical  conditions,  and  especi- 
ally, what  relations  exist  between  changes  of  rate  and  the 
typical  phenomena  of  melody.  Do  characteristic  changes 
accompany  the  perception  of  a  melodic  interval  which  is  felt 
to  lack  finality?  How  do  these  changes  differ  from  those  pro- 
duced by  an  interval  which  "ends?"  Does  a  succession  of 
two  tones  which  lack  melodic  "  relationship  "  have  a  peculiar 
effect?  What  of  the  "return?' '  What  of  disappointed  expec- 
tation? What  of  the  passage  to  a  tone  which  necessitates  a 
shift  of  tonality? 

,',  Tables  7  and  8  show  the  changes  in  rate  of  tapping  which 
accompany  the  hearing  of  the  melodic  interval  of  the  fourth, 
i.e.,  of  two  tones  whose  vibration  rates  are  in  the  ratio  3:4. 

1  L.  Hofbauer,  Arch.  f.  d.  ges.  Physiol.  (Pfluger's)  1897,  68,  546. 
2 Allen   Cleghorn,   "The  Reinforcement  of  Voluntary  Muscular  Contraction." 
Am.  Jour.  Physiol.     1898,  i,  338. 


58  W.  VAN  DYKE  BINGHAM. 

This  is  one  of  the  most  interesting  of  any  of  the  melodic  inter- 
vals from  a  psychological  point  of  view  because  of  the  strong 
sense  of  finality  which  it  gives  when  the  higher  tone  is  the  last. 
When  heard  as  a  descending  interval,  it  lacks  this  finality,  and 
yet  does  not  leave  one  wholly  in  suspense,  for  it  has  those  ele- 
ments of  finality  which  are  the  property  of  any  descending 
interval  as  such,  and  also  those  which  belong  to  every  tone  in 
the  tonic  chord.  Because  of  this  complexity,  judgments 
regarding  the  finality  of  the  descending  fourth  are  often  uncer- 
tain and  variable.  As  an  ascending  interval,  however,  there 
is  seldom  any  doubt  in  the  mind  of  the  observer  that  the  group 
is  a  completed  whole,  emphatically  coming  to  an  end.  It  is 
indeed  the  only  ascending  interval  of  which  so  broad  and  posi- 
tive an  assertion  can  be  made.  The  minor  second  and  minor 
sixth  are  the  only  other  intervals  at  all  comparable  with  it  in 
these  respects. 

The  tables  are  made  up,  as  were  the  previous  ones,  of  num- 
bers representing  the  metronome  rate  of  the  tapping  move- 
ment during  successive  periods  each  three  seconds  in  length. 
The  two  tones  were  each  sounded  for  three  seconds,  and  the 
numbers  immediately  under  the  letters  which  represent  the 
tones  consequently  express  the  rate  of  tapping  during  the 
course  of  the  melodic  stimulus.  To  call  attention  to  changes 
of  rate  at  critical  points  in  the  course  of  the  record,  use  is  made 
of  bold  faced  type  where  retardations  occur,  while  accelera- 
tions are  indicated  by  italics.  In  deciding  whether  or  not  a 
change  of  rate  accompanying  the  entrance  of  a  stimulus  was 
sufficient  in  amount  to  be  of  any  significance,  the  writer  has 
taken  into  account  the  degree  of  regularity  shown  in  the  tap- 
ping of  the  six  seconds  preceding,  but  has  neglected  the  period 
before  that,  which  was  often  so  near  the  beginning  of  the  tap- 
ping record  that  the  reagent  had  not  as  yet  found  his  pace. 

Examining  Table  7  with  reference  to  the  distribution  of 
retardations  and  accelerations  during  and  immediately  follow- 
ing the  melodic  stimulus,  one  notices  at  once  that  the  retarda- 
tions all  occur  during  the  sounding  of  the  tones  (six  during 
the  first  tone  and  two  during  the  second)  whereas  all  the  accel- 
erations are  found  within  the  period  of  the  last  tone  and  the 


STUDIES  IN  MELODY. 


S9 


period  immediately  after  it  (two  during,  and  six  after,  the  last 
tone). 

In  contrast  with  this  table  of  the  ascending  fourth,  the  table 
of  the  descending  fourth  exhibits  much  less  uniformity  in  the 
distribution  of  accelerations  and  retardations.  The  most 
striking  feature  is  the  large  proportion  of  retardations  which 
occur  during  or  immediately  after  the  sounding  of  the  second 
tone. 

TABLE  NO.  7 

Perfect  Fourth,  ascending.  Rate  of  tapping  during  successive  periods  of  three  seconds  each. 
Read  from  left  to  right.  Boldfaced  type  indicates  retardation  and  italics  acceleration,  at 
critical  points. 


d 


r 


Po 

Rg 

Rk 

Ho 

Fr 

Ta.... 

Pu 

'Stopped  tapping 


207 

94 

lOI 

10s 

190 

76 
118 


208 

95 
106 
103 
192 

75 
117 


212 

94 
104 
103 
186 

86 
120 


212 
91 

102 
92 

180 
73 

112 


92 
99 

93 
172 

72 
118 


225 
96 

lOI 
lOI 

185 

87 

122* 


223 

96 

96 

102 

179 

78 


220 

93 

99 

100 

183 

78 


TABLE  NO.  8 
Perfect  Fourth,  Descending. 


/' 

c' 

Po 

248 

91 
104 

95 
220 

82 
100 

255 
93 

lOI 

97 
214 

84 
106 

258 

95 
98 

99 
219 

8S 

263 

96 
103 

99 

213 

80 

258 
97 
103 
103 
210 
74 
101 

250 

96 
101 

104 
218 

73 
116 

256 
95 

lOI 

100 
213 

77 
114 

258 
04 

Rg 

Rk 

103 

Ho 

lOI 

Fr 

218 

Ta 

80 

Pu 

116 

§29  The  significance  of  these  facts  appears  when  they  are 
brought  into  comparison  with  the  results  of  the  previous  group 
of  experiments.  There  it  was  found  that  a  repetition  of  a  mus- 
ical sound  following  shortly  after  the  cessation  of  the  original 
stimulus  produces  effects  similar  to  those  of  the  first  sound, 
but  much  less  marked.  And  when  one  musical  sound  is  imme- 
diately followed  by  another  which  does  not  differ  from  it  in 


6o  W.  VAN  DYKE  BINGHAM. 

pitch  or  intensity  there  is  no  apparent  effect  upon  the  on-going 
activity,  the  only  changes  observable  being  in  the  direction  of 
a  return  to  the  natural  rate. 

When  successive  tonal  stimuli  differing  in  pitch  are  used — 
in  this  instance  two  tones  at  an  interval  of  a  fourth — the  char- 
acteristic variations  of  rate,  most  of  them  retardations,  follow 
the  entrance  of  the  first  tone;  but  when  this  is  succeeded  by 
the  second  tone,  one  does  not  find  the  same  absence  of  further 
variations  which  marked  the  appearance  of  a  second  tone  iden- 
tical in  pitch  with  the  first.  Instead  one  finds  fresh  changes  of 
rate;  and  upon  comparing  the  ascending  fourth  with  the  des- 
cending fourth  one  is  impressed  with  the  fact  that  the  accelera- 
tions belong  mainly  to  the  rising  interval,  while  most  of  the 
new  retardations  accompany  the  hearing  of  the  descending" 
fourth.  This,  it  will  be  born  in  mind,  is  an  interval  that  "ends" 
better  on  the  higher  tone. 

An  hypothesis  with  reference  to  the  significance  of  these 
motor  phenomena  may  here  be  briefly  outlined,  as  follows: 
(a)  Attention  is  an  activity  which  involves  both  special  and 
general  motor  adjustments,  (b)  The  general  aspects  of 
attentive  activity  are  of  such  a  nature  as  to  affect  general 
bodily  conditions;  and,  specifically,  (c)  the  rate  of  a  circular 
motor  process  (such  as  the  finger-movement)  which  is  going 
forward  semi-automatically,  will  be  affected  by  these  activi- 
ties, a  decrease  in  rate  signifying  inhibition,  due  to  increased 
activity  elsewhere,  and  an  acceleration  signifying  that  the 
task  of  attention  in  organizing  these  activities  is  being  suc- 
cessfully carried  out.  Retardation  or  inhibition,  it  is  to  be  ex- 
pected, will  enter  with  the  appearance  of  the  stimulus  demand- 
ing attention.  Continued  slow  rate  of  movement  will  result  if 
the  organizing  activities  of  the  attentive  process  continue  to 
meet  with  difficulties,  while  the  rate  will  be  augmented  as  the 
new  adjustments  come  to  be  efficiently  established. 

In  terms  of  this  hypothesis,  the  above  facts  with  reference 
to  the  hearing  of  the  rising  fourth  would  be  described  as  fol- 
lows :  Sudden  rise  in  the  level  of  attention  at  entrance  of  stim- 
ulus, continued  attentive  activity  during  the  sounding  of  the 
tones,  and  finally,  subsidence  of  attentive  activity  with  the 


STUDIES  IN  MELODY.  6 1 

satisfactory  completion  of  its  task;  or,  stated  differently,  pre- 
sentation of  a  problem  of  adjustment  as  stimulus  enters,  con- 
tinuance of  the  process  of  establishing  coordination  during  the 
sounding  of  tones,  and  then  increase  of  rate  signifying  the  effi- 
cient accomplishment  of  this  act. 

It  is  this  acceleration  accompanying  the  sense  of  finality 
I        which  seems  to  be  of  particular  significance. 

§30  In  testing  the  hypothesis,  the  introspections  of  the 
observers  must  be  taken  into  consideration,  for  not  always  is  a 
melodic  interval  heard  in  the  same  way.  What  an  interval  is 
to  the  observer  depends  as  much  upon  the  "attitude"  with 
which  it  is  received  as  it  does  upon  the  ratios  of  the  physical 
vibration  rates. ^ 

The  order  of  arrangement  of  the  observers  in  all  the  tables, 
it  will  be  recalled,  is  that  determined  by  the  tests  of  musical 
ability.  Po.,  the  most  musical,  reported  that  the  ascending 
fourth,  while  it  has  the  attribute  of  finality,  is  less  final  than 
some,  e.g.,  the  descending  fifth. 

"The  pitch  of  the  second  tone  came  as  a  surprise.  The  feeling  of 
satisfaction  came  only  toward  the  end  of  the  second  sound,  after  I  had 
got  it  placed  with  reference  to  the  first.  The  instant  of  entrance  of  the 
sense  of  satisfaction  was  very  marked. " 

(The  rate  for  the  first  four  taps  of  this  period  was  210,  for  the 
next  four  it  was  228  and  for  the  remaining  three,  232.)  This  ex- 
perience might  be  described  as  the  final  acceptance  of  a  second 
tone  as  a  tonic  which  when  first  heard  was  not  so  construed. 
If,  during  the  hearing  of  the  first  tone,  a  tonality  feeling  gets 
established  with  this  tone  as  a  tonic — as  is  very  frequently  the 
case — the  transition  to  a  tone  of  different  pitch  presents  three 
possibilities,  (a)  It  may  be  an  "unrelated"  tone,  foreign  not 
only  to  the  tonality  already  in  mind  but  also  to  any  other  tonal- 
ity within  which  the  first  tone  would  find  a  place.  In  such  an 
instance  there  can  be  no  melody  feeling,^  for  there  is  no  coher- 
ence or  relevance  between  the  tones;  they  do  not  tend  to  insti- 

^Cf.  supra,  p.  32/. 

2  Here,  and  throughout  the  discussion  of  the  experiments,  it  will  be  understood 
that  these  statements  are  made  solely  with  reference  to  the  experience  of  observers 
who  are  familiar  with  a  harmonic  musical  system. 


62  W.  VAN  DYKE  BINGHAM. 

tute  a  common  set  of  expectations;  they  do  not  belong  to  the 
same  whole,  (b)  The  second  of  the  two  tones  may  be  "related" 
to  the  first  as  to  a  tonic.  It  belongs  to  the  tonality  already  in 
mind,  and  consequently  it  is  welcomed,  as  partially  satisfying 
the  expectations  of  the  hearer;  but  it  does  not  wholly  satisfy 
them.  Instead,  it  only  makes  more  definite  and  insistent  the 
demand  that  the  first  tone  shall  be  heard  again,  at  the  end  of  the 
melody;  it  intensifies  the  original  tonality  feeling.  If  the  se- 
quence of  tones  ends  here,  one  experiences  the  feeling  of  unrest 
and  dissatisfaction  which  accompanies  disappointed  expecta- 
tion or  thwarted  intent,  (c)  The  second  tone  may  be  capable 
of  entering  into  tonality  relations  with  the  first,  but  not  into  the 
tonality  of  which  that  tone  is  the  tonic.  This  necessitates  a 
shift  of  tonality.  In  place  of  the  organized  set  of  expectations 
already  present,  a  different  set  appears.  The  extreme  instance 
of  this  peculiarly  subtile  and  elusive  process  occurs  when  the 
second  tone  becomes  itself  the  tonic  of  a  new  tonality,  usurping 
the  power  and  function  originally  held  by  its  predecessor,  and 
organizing  a  new  set  of  expectations.  Such  an  instance  is 
found  in  the  interval  of  the  ascending  fourth. 

Po.  was  probably  not  the  only  observer  who  experienced  this 
peculiar  shift  of  tonality  upon  hearing  the  interval  of  the 
ascending  fourth ;  but  he  is  the  only  one  who  detected  and  de- 
scribed the  feeling  of  transition  and  the  satisfaction  which  fol- 
lowed. Rg.  reported  that  the  interval  seemed  to  him  to  be 
rather  indifferent,  but  after  hearing  fc'  he  said  that  c'f  had 
more  finality  about  it  than  he  had  thought  at  first.  Rk. 
reports,  "That  sounds  like  'sol  do' ;  there  is  no  need  of  a  third 
tone."  Ho.  " That  ends !  It  is  very  agreeable."  Fr.  "That's 
all  right."  Ta.  found  it  difficult  to  give  an  introspective 
report.  The  interval  he  said  was  elusive,  and  it  was  hard  to 
say  just  what  the  effect  was.  Pu.  reported  no  definite  effect 
of  any  sort.  It  must  be  noted  that  even  in  the  case  of  these 
last  two  observers  an  acceleration  of  rate  occurred  immediately 
after  the  close  of  the  tone. 

With  the  descending  fourth  we  find  much  less  uniformity  in 
the  distribution  of  accelerations  and  retardations,  and  also  a 
greater  diversity  in   the   introspective  reports.     The  most 


STUDIES  IN  MELODY.  63 

Striking  and  important  feature  is  the  large  proportion  of  retar- 
dations which  occur  during  or  immediately  after  the  sounding 
of  the  second  tone.  Po.  reports  that  the  interval  was  pleas- 
ing, but  not  wholly  satisfactory  because  it  lacked  finality. 
During  the  sounding  of  the  second  tone  his  rate  recovered 
from  the  slowing-up  produced  by  the  first  tone  but  after  the 
melody  ended  there  was  a  retardation.  For  Rg.  the  interval 
lacked  finality  but  as  to  agreeableness  it  was  indifferent. 
Rk.'s  introspections  were  interesting.  "That  is  all  right,  but 
I  can't  help  thinking  in  three's."  That  is  to  say,  he  gave  an 
intellectual  judgment  that  the  interval  was  complete  but 
really  felt  a  need  for  something  further.  (Note  the  retardation 
in  rate.)  Ho.  says,  "  I  should  like  to  add  a  third  note  but  it  is 
not  bad."  Fr.,  "Unfinished,  but  pleasant  as  far  as  it  goes." 
Ta.  "I  cannot  decide.  I  keep  changing  my  mind.  It  is  a 
puzzling  interval."  Pu.,  "Very  definitely  complete  and 
pleasant." 

If  one  examines  the  table  in  the  light  of  these  introspective 
comments,  it  is  found  that  five  of  the  seven  records  support 
our  hypothesis  with  reference  to  the  motor  effect  of  the  finality 
experience. 

With  all  of  the  remaining  tables  the  introspections  are  pre- 
sented in  very  brief  summary.  The  observer's  own  words  are 
used,  as  far  as  the  necessities  of  condensation  allow. 

§31  Tables  9  and  10  should  be  examined  together.  They 
show  the  effects  produced  by  the  melodic  interval  of  the  per- 
fect fifth,  ascending  and  descending.  With  regard  to  the 
aspect  of  finality,  all  the  observers  with  the  exception  of  the 
two  least  musical  ones  are  agreed  that  the  ascending  fifth  is 
lacking  in  completeness.  In  spite  of  this  fact,  the  proportion 
of  retardations  and  accelerations  during  the  period  while  the 
second  tone  was  sounding  and  immediately  after,  do  not  show 
a'balance  in  favor  of  the  retardations.  The  lack  of  finality  in 
this  interval  is  not  sufficiently  marked  to  produce  the  vivid 
experiences  of  tension  which  characterize  the  perception  of 
some  melodic  intervals.  A  more  significant  reason  why  one 
should  not  expect  a  larger  proportion  of  retardations  here,  will 
become  evident  shortly. 


64 


W.  VAN  DYKE  BINGHAM. 
TABLE  NO.  9 


Perfect  Fifth,  Ascending.  Rate  of  tapping  during  successive  periods  of  three  seconds  each. 
Read  from  left  to  right.  Numbers  showing  decrease  in  rate  at  critical  points  in  the  record 
are  printed  in  bold  face  type.    Increases  in  rate  are  printed  in  italics. 


d 


g' 


Po, 

Rg 
Rk 
Ho 
Fr. 
Ta 
Pu 


225 
129 
117 
102 
234 
73 
102 


224 
130 
117 
no 
233 
74 
109 


225 
127 
118 
III 

23s 

76 

108 


224 
126 
119 
104 

237 

71 

106 


228 

I2S 

116 

96 

231 

77 
III 


236 
132 

"5 
102 
232 
80 
104 


236 
124 
114 
los 
226 
81 
103 


230 
128 
118 
104 
230 
83 


Introspections. 

Po.  A  sense  of  finality,  but  not  completely  final.     Pleasant. 

Rg.  A  beginning,  not  an  end.     Wanted  to  go  on. 

Rk.  Want  to  hear  first  again. 

Ho.  Needs  third  tone.     Not  extremely  bad. 

Fr.  Unfinished.     Pleasant. 

Ta.  That  is  finished!     Felt  so  the  instant  it  sounded. 

Pu.  Fairly  complete.     Agreeable  ending,  but  I  do  not  like  so  wide  an  interval. 

TABLE  NO.   10 
Perfect  Fifth,  descending. 


g' 


Po 

Rg 

Rk 

Ho 

Fr 

Ta 

Pu 

'Stopped  Tapping 


197 

204 

208 

204 

208 

214 

219 

129 

125 

ns 

132 

126 

134 

133 

106 

108 

108 

102 

lOI 

105 

103 

109 

"3 

III 

107 

106 

log 

* 

234 

225 

220 

221 

220 

220 

222 

78 

78 

78 

78 

78 

83 

83 

103 

106 

"3 

101 

97 

112 

104 

220 

143 
105 

229 

82 


Introspections. 


Po.  No  suggestion  of  further  movement.     Satisfactory. 

Rg.  Left  no  impression. 

Rk.  Doesn't  need  a  third.     Pleasant. 

Ho.  Can't  say  as  to  finahty.     Fairly  agreeable. 

Fr,  Incoherent.     Unfinished.     Unpleasant. 

Ta.  (Introspection  uncertain.) 

Pu.  Did  not  demand  third  note. 


STUDIES  IN  MELODY. 


65 


Table  10,  the  descending  fifth,  presents  a  much  more  uni- 
form appearance.  Accelerations  following  the  close  of  the 
melody  occur  in  every  record  except  that  of  Fr.,  which  shows 
no  change  in  rate  at  this  point.  The  introspections,  however, 
are  not  as  definite,  three  observers  failing  to  report  anything 
positive  regarding  the  finished,  self-complete  character  of  the 
melody.  The  only  one,  however,  who  found  the  melody 
incomplete  was  Fr.,  the  observer  whose  rate  is  the  only  one  to 
show  no  increase  at  this  point. 


TABLE  NO.  n 


Perfect  Fifth,  descending.     Three  tones  expected.    Average  rate  of  tapping  by  three-second 
periods.    Read  from  left  to  right. 

g'         e 


Po 
Rk 

Rg 
Ho 
Ta 
Pu 


284 

284 

275 

277 

275 

267 

269 

269 

205 

202 

206 

202 

204 

194 

197 

223 

112 

117 

117 

113 

112 

128 

118 

127 

108 

no 

III 

in 

106 

101 

99 

100 

76 

76 

77 

68 

70 

73 

75 

73 

104 

108 

108 

100 

108 

100 

lOI 

104 

1 

^ntrospec 

tions. 

Po.  Amusing.     Incomplete. 

Rg.  A  feeling  of  incompleteness. 

Rk.  Disappointing. 

Ho.  Unfinished,  because  of  expectancy  of  another  tone.  ♦ 

Ta.  Incomplete.    Thought  you  were  trying  to  fool  me. 

Pu.  Surprised  that  there  were  not  three.    Incomplete. 

The  records  from  which  Table  1 1  were  prepared  were  taken 
at  the  end  of  the  year's  experimenting  because  it  was  desired 
to  avoid  the  suspicious  attitude  which  it  might  possibly  have 
induced  in  some  observers.  One  of  the  details  of  method,  it 
will  be  recalled,  was  to  let  the  observer  know  beforehand  how 
many  tones  were  to  be  expected,  in  order  to  keep  the  conditions 
-in  this  respect  as  constant  as  possible.  In  this  final  experi- 
ment, however,  the  observer  was  led  to  expect  three  tones, 
but  only  two  were  given,  the  same  two  used  in  the  experiment 
just  described.  (Table  10).  Any  changes  in  rate  of  tapping 
produced  by  unfulfilled  expectation  ought  then  to  become  evi- 
dent by  a  comparison  of  these  two  tables,  9  and  10,  and  indeed 


66 


W.  VAN  DYKE  BINGHAM. 


the  diflFerence  is  sufficiently  striking.  Instead  of  uniform 
accelerations  following  the  tones  one  finds  retardations  in 
nearly  every  instance. 

This,  then,  may  aid  us  in  understanding  the  accelerations  so 
frequently  found  where  introspection  reports  that  the  interval 
lacks  finality.  As  a  melodic  interval  it  is  left  unfinished,  but 
in  so  far  as  the  hearer  was  expecting  a  certain  number  of  tones 
and  that  expectation  was  fulfilled,  the  experience  as  a  whole 
gets  a  certain  completeness  and  unity.  Part,  at  least,  of  the 
adjustments  of  attention  have  functioned  as  intended,  and 
only  so  much  of  the  total  motor  attitude  as  was  immediately 
concerned  with  the  tonality  experience  as  such  has  to  be  re-ad- 
justed when  the  melody  comes  to  an  end  on  what  is  not  a  final 
tone. 

The  diminished  fifth  (45:64)  was  selected  as  an  example 
of  a  group  of  two  "unrelated"  tones.  The  testimony  of  the 
observers  is  nearly  unanimous  that  the  interval  lacks  complete- 
ness and  is  disagreeable  to  hear  both  ascending  and  descending. 
(Tables  12  and  13.)  Nevertheless  there  are  a  larger  number  of 
accelerations  than  of  retardations.  A  comparison  of  the 
''exceptions"  with  those  in  the  introspective  table  clears  up  the 
difficulty  somewhat,  but  even  then  it  must  be  said  that  this 
pair  of  tables  tells  against  our  hypothesis.     The  only  recourse 

TABLE  NO.  12 
Diminished  Fifth,  ascending.    Average  rate  by  three-second  periods.    Read  across. 


r 


Po 

Rg 

Fr. 
Ta 
Pu 


265 

274 

277 

270 

267 

270 

270 

122 

114 

118 

122 

126 

117 

116 

247 

232 

232 

242 

233 

247 

239 

76 

80 

78 

72 

73 

76 

78 

74 

73 

75 

66 

76 

79 

79 

265 
115 

240 
77 
84 


Po.    A  raw  rough  interval 

Incomplete. 
Rg.     Disagreeable  because  incomplete. 
Fr.    Not  finished  but  good  as  far  as  it  went. 
Ta.     Unfinished  but  a  pleasant  interval. 
Pu.    Very  disagreeable.     Felt  at  entrance  of  second  tone. 


Introspections. 
Associations  with  Wagner  made  it  less  disagreeable. 


STUDIES  IN  MELODY. 


67 


TABLE  NO.  13 
Diminished  Fifth,  descending.    Average  rate  by  three-second  periods.    Read  across. 

f  b 


Po 

Rg 

Fr. 
Ta 
Pu 


263 

276 

265 

263 

267 

274 

270 

116 

118 

117 

"S 

131 

130 

131 

192 

200 

219 

207 

198 

192 

202 

76 

78 

76 

70 

71 

76 

74 

80 

79 

77 

79 

76 

82 

85 

267 

119 

211 
76 

77 


Po. 

Rg. 

Fr. 
two. 
Ta. 
Pu. 

sure. 


Introspections 

Incomplete,  but  not  seriously  so. 

One  more  tone  (he  hummed  c)  would  make  a  great  difference. 

Very  unpleasant.    It  seemed  complete  because  you  told  me  there  would  be  but 


Finished.    A  pleasant  interval. 
Didn't  think  about  completeness. 


At  first  thought  it  disagreeable,  then  not 


is  to  the  principle  that  the  tapping  tends  to  become  rapid 
whenever  attention  is  freed  from  the  stimulus,  irrespective 
of  what  the  stimulus  may  be. 

The  descending  major  third  is  an  emphatically  final  melody 
(although  Fr.  and  Pu.  did  not  so  describe  it),  and  the  table 
(No.  14)  shows  the  expected  accelerations.  The  most  inter- 
esting feature  is,  however,  the  marked  retardation  in  the 
record  of  Rk.  The  last  tone  was  a  final  tone,  he  said,  but 
he  wanted  a  third  tone  in  between  the  first  and  second,  and 
tried  to  figure  out  what  tone  that  should  be.  The  retarda- 
tion occurs  in  the  portion  of  the  record  where  this  was  being 
done. 

In  this  and  several  of  the  following  tables  are  given  the 
measurements  of  a  single  record  in  which  the  rate  of  each 
separate  tap  is  determined.  Samples  of  the  tapping  of  each 
of  the  different  observers  are  thus  made  available  for  detailed 
. Inspection.  It  is  interesting  that  the  rate  for  individual  taps 
can  fluctuate  as  widely  as  it  does  without  greater  variability 
in  the  rate  as  measured  for  periods  of  three  seconds. 

The  minor  sixth  (5  :  8)  was,  somewhat  to  the  surprise  of 
the  experimenter,  judged  to  be  an  incqmplete  and  disappoint- 
ing melody,  ascending  as  well  as  descending.     It  has  the 


68 


W.  VAN  DYKE  BINGHAM. 


TABLE  NO.   14 
Major  Third,  descending.    Metronome  rate  of  each  separate  tap.    Read  down. 


Rk. 


177 

187 

202 

198 

218 

178 

148 

181 

163 

206 

191 

202 

149 

148 

168 

182 

202 

i8s 

IS3 

148 

246 

177 

160 

179 

191 

171 

159 

198 

181 

164 

185 

211 

176 

162 

182 

176 

182 

160 

209 

182 

148 

153 

182 

153 

190 

271 

163 

159 

191 

177 

171 

197 

202 

132 

148 

185 

182 

182 

166 

226 

183 

183 

172 

182 

185 

188 
171 

169 

158 

172 

148 


Average  rate  for  each  three-second  period.    Read  across. 


Rk. 
Po. 
Ho. 
Fr. 
Pu. 


178 

171 

185 

207 

188 

162 

176 

225 

222 

225 

227 

229 

237 

230 

100 

103 

104 

98 

97 

106 

106 

193 

195 

209 

205 

206 

213 

195 

80 

81 

85 

77 

80 

88 

84 

171 
237 

102 

214 

86 


Introspections. 

Rk.  Wanted  a  third  tone  between.    Tried  to  decide  what  it  should  be. 

Po.  Surprising,  but  very  satisfying.     Final. 

Ho.  It  became  satisfactorily  complete  after  I  had  thought  about  it. 

Fr.  Coherent,  but  suggested  something  further. 

Pu.  Needed  a  third  tone  to  complete  it; 

TABLE  NO.  16 

Minor  Sixth,  descending.    Metronome  rate  of  each  separate  tap.    Read  down. 


Ho. 


106 

103 

"3 

119 

109 

105 

92 

III 

117 

106 

"5 

104 

89 

100 

103 

119 

82 

96 

los 

lOI 

no 

102 

114 

106 

no 

117 

123 

106 

128 

lOI 

97 

102 

III 

no 

III 

no 

I" 

89 

106 

89 

Average  rate  by  three-second  periods.     Read  across. 


Po. 
Rk. 
Ho. 
Fr. 
Ta. 
Pu. 


225 

220 

224 

204 

222 

222 

225 

227 

137 

128 

^35 

139 

145 

130 

130 

137 

104 

106 

"3 

108 

108 

99 

lOI 

loS 

172 

158 

181 

175 

183 

183 

184 

182 

106 

lOI 

los 

105 

107 

100 

103 

105 

112 

in 

112 

114 

127 

118 

122 

I2S 

STUDIES  IN  MELODY. 


69 


Introspections 

Po.  Surprise  and  disappointment  on  second  tone.     Unsatisfactory. 

Rk.  Does  not  end. 

Ho.  Very  noticeably  lacked  finality. 

Fr.  Quite  unrelated. 

Ta.  Tone  pleasant  but  melody  does  not  end. 

Pu.  Unsatisfactory.     Incomplete. 

TABLE  NO.   16 
Minor  Sixth,  ascending.    Metronome  rate  of  each  separate  tap.      Read  down 


b               g' 

Ta 

80 

86 

75 

81 

n 

79 

79 

81 

86 

81 

83 

72 

82 

77 

79 

79 

82 

81 

83 

72 

79 

81 

81 

82 

81 

82 

82 

73 

71 

86 

81 

75 

A  verage  rate  by  three-second  periods.    Read  across. 

*      «' 

Rg 
Ho 
Fr. 
Ta 
Pu 


99 

lOI 

104 

98 

lOI 

97 

99 

102 

108 

no 

102 

98 

98 

98 

208 

207 

215 

223 

215 

208 

201 

82 

82 

81 

74 

77 

81 

80 

97 

97 

97 

96 

95 

100 

102 

100 
100 
213 

79 
107 


Introspections 

Rg.  No  melody;  no  finality. 

Ho.  Seemed  bad  at  first  but  changes  to  a  final  interval. 

Fr.  Unconnected  and  therefore  unpleasant. 

Ta.  Incomplete. 

Pu.  Unrelated.     The  second  note  seemed  to  change  in  character. 

character  of  incompleteness  very  strongly  as  a  descending 
interval,  but  when  heard  in  the  opposite  direction  it  is  possible 
so  to  reconstruct  the  tonality  as  to  make  the  higher  tone  a 
tonic.  This,  the  observers,  with  a  single  exception,  failed 
to  do. 

",  Consequently  Tables  15  and  16  may  both  be  taken  as 
showing  the  effects  of  a  melody  that  lacks  finality.  The 
unusually  large  number  of  retardations  strikes  the  eye  at  a 
glance. 

§32     Turning  now  to  some  examples  of  three-tone  groups 
(tables  17  and  18),  we  are  confronted  at  the  outset  with  the 


70 


W.  VAN  DYKE  BINGHAM. 


difficulty  that  it  is  usually  quite  possible  to  interpret  any 
group  of  three  related  tones  in  a  variety  of  ways,  and  we  are 
thrown  back  upon  the  introspections  of  the  observers  for  a 
starting  point  in  our  interpretation  of  the  results.  This 
method  has  its  obvious  disadvantages,  notably  those  result- 
ing from  the  probably  imperfect  reports  which  the  average 
observer  can  give  about  so  complex  an  experience  as  the 
course  of  a  three-tone  melody. 

TABLE   NO.    17 
Three- tone  groups .    Average  rate  for  each  three-second  period .     Read  across. 


Rk 
Ho 
Ta 
Pu 


140 

143 

141 

142 

141 

146 

153 

147 

122 

118 

116 

109 

117 

118 

n6 

118 

71 

74 

71 

70 

76 

87 

88 

75 

123 

120 

13s 

114 

128 

127 

127 

121 

142 

112 

72 

138 


Introspections 


Rk.  Finished.     Very  good  melody. 

Ho.  Complete,  satisfactory. 

Ta.  Incomplete. 

Pu.  Uncertain. 


TABLE  NO.  18 


g 

,.b' 

hb 

Rk 

130 

131 

126 

132 

139 

151 

170 

139 

136 

Ho 

no 

118 

"3 

112 

IIS 

111 

118 

112 

118 

Ta 

70 

70 

68 

63 

67 

76 

66 

66 

66 

Pu 

145 

144 

154 

138 

142 

148 

141 

146 

151 

Introspections 

Rk.  Leaves  me  in  suspense. 

Ho.  Unfinished.     Don't  like  it. 

Ta.  Second  note  did  not  fit  in  at  all.     Very  disconnected. 

Pu.  Fairly  good  ending,  but  the  intervals  are  too  wide. 


The  two  melodies  placed  together  here  for  comparison  are 
very  similar  in  form,  and  both  are  made  up  of  wide,  conso- 
nant intervals,  but  one  of  them,  the  first,  seemed  to  the  experi- 
menter to  have  a  more  positive  finality.     The  more  musical 


STUDIES  IN  MELODY. 


71 


observers  agree  with  him  in  this.  All  of  the  retardations 
(neglecting  of  course  those  which  accompany  the  entrance  of 
the  first  tone)  occur  at  the  end  of  the  less  final  of  the  two 
melodies. 

On  the  whole  these  tables  are  not  very  illuminating. 

TABLE  no:      19 
Three-tone  groups.    Averagerate  for  each  three-second  period.    Read  across. 


c' 

a 

b 

Rk 

154 

152 

160 

164 

159 

^74 

166 

179 

160 

Ho 

"5 

107 

109 

112 

105 

86 

96 

no 

104 

Ta 

69 

71 

71 

70 

71 

72 

70 

70 

71 

Pu 

103 

loS 

los 

% 

102 

lOI 

log 

114 

114 

Rk.    Unsatisfactory.    Must  go  back  to  first  tone. 

Ho.    Perfectly  horrid!    Due  to  the  last  tone. 

Ta.     Could  give  no  introspection.     (Note  regularity  of  rate.) 

Pu.     Indifferent. 

TABLE    NO.   20 


c' 

a 

tb 

I  Rk 

164 

160 

159 

173 

168 

180 

170 

177 

168 

2  Rk 

159 

156 

IS7 

149 

145 

146 

155 

171 

168 

3  Rk 

178 

180 

184 

179 

180 

187 

188 

181 

181 

Ho 

97 

102 

106 

104 

99 

103 

lOI 

100 

104 

Ta 

77 

80 

77 

73 

75 

87 

85 

78 

85 

Pu 

97 

99 

98 

100 

97 

III 

106 

99 

98 

1.  Rk.    Wrong,  but  not  very  bad.     Second  note  spoiled  it. 

2.  Rk  and  3  Rk.  (repetitions  at  a  later  date  of  same  tones.)     Both  satisfactory  and  com- 

plete, the  latter  reassuringly  so. 
Ho.    Last  note  predominates  and  becomes  satisfactory  ending, 
Ta.    Indifferent  ending.    Last  note  a  disappointment. 
Pu.    Tones  seemed  disconnected. 

Table  20  is  of  interest  mainly  because  it  shows  the  different 
reactions  which  the  same  melody  elicited  from  one  of  the 
subjects  at  different  times.  The  group  of  intervals,  c'-a-bb, 
is  one  which  demands  a  shift  of  tonality,  but  which  then  ends, 
satisfactorily.  When  it  was  first  given,  Rk.  did  not  so  hear 
the  melody:  the  tonality  did  not  become  readjusted.  Two 
weeks  later  the  experiment  was  repeated  and  this  time  the 
tones  were  heard  as  a  complete  melody.  It  was  immediately 
given  again,  with    similar   but  more  positive  introspective 


72 


W.  VAN  DYKE  BINGHAM. 


reports  as  the  result.  The  three  records  show  the  expected 
differences  in  the  tapping. 

A  striking  record  is  that  of  Ta.  (Table  19).  He  tapped 
throughout  the  course  of  the  experiment  almost  with  the 
regularity  of  a  ruling  engine.  When  asked  for  an  introspec- 
tive report,  he  could  find  nothing  to  say !  The  tones  had  had 
no  effect  whatever. 

Every  retardation  shown  in  these  tables  finds  its  explanation 
in  the  introspective  records.  Not  quite  as  much  can  be  said 
for  all  of  the  accelerations. 

With  table  21  we  take  up  the  study  of  the  "Return."  The 
interval  here  used  is  the  major  second  (8:  9).  This  is  a  very 
satisfactory  melodic  figure  when  the  lower  tone  is  the  start- 

TABLE  NO.  21 

Three-tone  group.  Major  second.  Average  rate  for  each  three-second  period.  Read 
across. 


d' 


d' 


Po. 
Rk 
Ho 
Ta 
Pu 


248 

244 

249 

242 

218 

229 

244 

253 

192 

19s 

191 

171 

170 

170 

176 

183 

109 

lOI 

102 

93 

96 

92 

98 

98 

100 

107 

112 

103 

98 

J02 

99 

lOI 

95 

94 

98 

89 

91 

lOI 

105 

lOI 

251 
187 

102 

lOI 

103 


Po.     Second  tone  very  unpleasant.    Third  reinstated  calm  and  repose  of  the  first.     At 

loose  ends  on  second.    The  return  changed  all  this. 
Rk.     Very  unsatisfactory  as  a  whole  but  had  a  certain  unity  about  it. 
Ho.    I  think  that  ended  nicely.     It  is  curious  that  I  can  not  recall  the  middle  tone. 
Ta.    The  lower  would  have  been  a  better  ending. 
Pu.     Second  note  not  right.     Return  to  first  gave  feeling  of  finality. 

TABLE  NO.  22 


d' 


Po. 
Rk. 
Ho. 
Ta. 
Pu. 


259 

265 

26s 

259 

254 

261 

256 

265 

162 

188 

181 

164 

158 

171 

178 

192 

114 

loS 

no 

97 

100 

93 

100 

93 

114 

106 

101 

107 

95 

102 

102 

121 

106 

118 

102 

III 

96 

95 

108 

100 

252 
181 

"5 
102 


Po.  Third  tone  a  pleasant  relief  from  suspense. 

Rk.  It  was  all  right  at  the  time. 

Ho.  Very  pleasant  and  complete. 

Ta.  Positively  finished. 

Pu.  Pleasant  and  complete. 


STUDIES  IN  MELODY. 


73 


ing  point  and  the  end,  and  one  is  not  surprised  to  find  a  large 
proportion  of  accelerations  at  the  close.  (See  table  22,  c'- 
d'-c'.)     The  record  fits   well  with  the  introspections. 

When  the  upper  tone  is  made  the  point  of  departure  and 
return,  the  melody  tends  to  fall  apart.  The  middle  tone 
positively  will  not  fit  into  any  tonality  suggested  by  the  first. 
This  appears  very  prominently  in  the  introspective  records. 
Another  feature  is  that  without  exception  the  observers  felt 
that  the  return  from  this  lower  tone  to  the  upper  was  very 
satisfactory.  "The  third  reinstated  the  calm  and  repose  of 
the  first,"  etc.  The  entire  set  of  introspections  accompany- 
ing this  table  is  recommended  for  careful  perusal  as  clearly 
setting  forth  the  result  of  a  return  from  a  tone  felt  to  be 
foreign  to  the  first.  The  experience  acquires  a  unity  which  is 
most  certainly  not  contributed  by  any  interval  "relationship." 

TABLE  NO.  23 

Three-tone  groups.    "The  Return."    Average  rate  for  each  three-second  period.    Read 


d 

/' 

c' 

Po 

28s 

260 

254 

259 

244 

238 

248 

256 

258 

Rk 

154 

162 

164 

168 

160 

171 

178 

176 

167 

Ta 

82 

83 

81 

76 

79 

78 

74 

76 

84 

Pu 

99 

105 

no 

% 

no 

99 

113 

107 

108 

Po. 
Rk. 
Ta. 
Pu. 


Introspectiovs. 

Much  less  complete  than  if  upper  tone  were  last. 

Satisfactory  ending,  but  not  so  good  as  f-c-f  (hummed). 

Finished. 

Incomplete.     Second  tone  unrelated  to  others. 

TABLE  NO.  24 


/' 


/' 


Po. 

Rg 

Rk. 

Ta. 
'pu. 


249 

249 

249 

236 

234 

254 

259 

261 

119 

126 

126 

123 

127 

123 

126 

128 

171 

180 

183 

172 

170 

176 

176 

181 

79 

76 

75 

72 

70 

73 

72 

75 

81 

86 

87 

90 

86 

go 

lOI 

97 

262 
126 

76 
96 


Po. 

Rg- 

Rk. 

Ta. 
Pu. 


Emphatically  final. 
O.  K.     Finished. 
Fairly  satisfactory. 
Fairly  complete. 
Complete. 


More  so  than  c-f-c  (hummed). 


74 


W.  VAN  DYKE  BINGHAM. 
TABLE  NO.  25 

Three-tone  groups.     "The  Return." 
Rate  for  each  separate  tap.     Read  down. 


Po. 


c' 

g' 

c' 

243 

274 

242 

240 

267 

236 

248 

236 

28s 

267 

246 

253 

236 

254 

246 

229 

262 

258 

226 

260 

240 

244 

276 

204 

265 

260 

226 

247 

256 

252 

265 

223 

258 

222 

239 

252 

276 

254 

263 

213 

260 

232 

221 

262 

262 

269 

236 

229 

272 

252 

224 

248 

267 

278 

247 

256 

265 

254 

253 

233 

260 

250 

260 

265 

260 

236 

236 

233 

231 

250 

252 

260 

276 

221 

236 

252 

269 

248 

233 

256 

272 

224 

258 

276 

277 

224 

270 

250 

269 

232 

242 

272 

256 

228 

260 

258 

272 

226 

240 

272 

258 

240 

234 

246 

252 
267 
267 
246 
242 

254 

254 
243 
267 
240 
272 
253 
254 


Three-tone  groups. 

"TheReturn." 

A  verage  rate  by  three-second  periods.    Read  across . 

c'     g'            c' 

Po 

268 

238 

238 

254 

258 

248 

251 

240 

254 

Rk 

118 

118 

119 

116 

118 

128 

115 

117 

Ho 

79 

80 

79 

78 

80 

82 

93 

95 

95 

Fr 

208 

203 

200 

199 

196 

206 

207 

200 

198 

Po. 
Rk. 
Ho. 
Fr. 


Introspections. 
Not  very  good. 


More  or  less  complete 
O.  K.     Finished. 
Complete.     Very  pleasant. 
Complete,  but  not  wholly  satisfactory, 


A  study  of  the  table  of  rates  itself  is  equally  illuminating. 
In  number  and  distribution  of  accelerations,  it  is  almost 
identical  with  the  companion  table,  where  the  return  was 
from  a  tone  felt  to  be  quite  coherent  with  the  first  tone  of 
the  melody. 

Tables  23-26  also  show  the  effects  of  the  return  to  the  start- 
ing point.  The  intervals  used  differ  from  the  preceding  in 
that  they  are  wider,  and  consonant  intervals.  The  fourth 
(tables  23  -and  24)  ends  more  emphatically  upon  the  upper 
note,  the  fifth  (tables  25  and  26)  on  the  lower.  This  was  the 
judgment  of  the  observers.     The  small  sprinkling  of  retarda- 


STUDIES  IN  MELODY. 


75 


tions  at  the  close  of  these  melodies  would  indicate  that  this 
difiference  in  finality  is  unable  to  maintain  itself,as  against 
the  two  factors  that  tend  to  exert  an  opposing  influence  upon 
the  tapping,  the  factors,  namely,  of  the  return,  and  of  the 
fact  that  the  expected  number  of  tones  was  heard  and  nothing 
further  anticipated. 


TABLE  NO.  26 

g'        c 

g' 

Po 

230 

138 

77 

204 

74 
106 

230 
138 

78 
197 

74 

237 

140 

80 

196 

107 

227 
131 

79 
197 

74 
103 

208 

140 

77 

193 

73 
102 

239 

139 

■  80 

195 

76 

116 

246 
136 

86 

193 

81 

119 

251 
128 

84 
196 

75 
no 

Rk 

Ho 

Fr 

203 

81 

108 

Ta 

Pu 

Po.  No  feeling  of  finality;  therefore  unpleasant.     No  tendency  to   go   elsewhere. 

Rk.  Not  as  complete  as  c'-g'-c'  (hummed),  but  one  isn't  left  in  suspense. 

Ho.  Can't  say  as  to  completeness.     Unpleasant. 

Fr.  Incomplete. 

Ta.  Better  to  end  on  second  note. 

Pu.  Not  emphatic  finality;  only  such  as  any '  return'  gives. 

What  of  the  octave?  Meyer  was  unable  to  detect  any 
stronger  "trend"  to  the  lower  than  to  the  upper  tone,  and 
consequently  put  himself  on  record  as  opposed  to  Lipps  and 
the  other  writers  who  assert  that  the  lower  tone  possesses  the 
stronger  finality.^ 

The  question  was  put  to  each  of  my  observers.  They  were 
asked  to  judge  with  reference  to  the  finality  of  ascending 
octaves,  descending  octaves,  and  also  groups  of  three  tones, 
involving  the  return.  Intervals  in  the  middle  region  of  the 
scale  and  also  in  the  great  octave  were  used.  The  results  were 
strongly  against  Meyer's  view.  Pu.,  the  least  musical  of  the 
observers,  could  detect  no  difference  in  finality  between  the 
end  on  the  upper  and  the  end  on  the  lower  of  two  tones  an 
octave  apart.  All  others  found  that  a  stronger  feeling  of 
finality  attached  to  the  end  on  the  lower  tone.     This  dif- 

1  Psych.  Rev.  1900,  7,  248.  In  the  light  of  his  more  recent  studies  on  the  effect  of 
the  falling  inflection  (see  above,  p.  28)  we  suspect  that  Meyer  would  today  formulate 
somewhat  more  guardedly  his  statements  regarding  the  psychological  effect  of  the  dose 
on  "i"  and  on  "2." 


76 


W.  VAN  DYKE  BINGHAM. 


ference  of  preference  does  not  make  itself  evident,  however, 
in  the  tapping  records  of  tables  27  and  28  (the  octave).  At 
the  close  of  the  melody  there  is  found  almost  exactly  the  same 
preponderance  of  accelerations  over  retardations  in  each  of 
the  two  tables.     Although  one  ending  is  better,  both  are  good . 

TABLE    NO.    27 
The  Octave.    Rate  of  each  separate  tap.    Read  down. 


Rg. 


90 

93 

96 

88 

83 

70 

81 

85 

81 

83 

93 

8S 

93 

83 

92 

93 

88 

88 

95 

93 

81 

88 

97 

83 

93 

88 

88 

81 

79 

8i 

86 

90 

86 
90 
83 
8S 


Average  rate  for  each  three-second  period.    Read  across. 


c" 


c' 


Rg 

Po. 
Rk 
Ho 
Fr. 
Ta. 
Pu. 


88 

88 

93 

86 

83 

8S 

88 

88 

258 

252 

254 

246 

238 

239 

257 

256 

238 

232 

236 

211 

204 

205 

210 

218 

120 

120 

119 

104 

108 

109 

96 

107 

186 

199 

199 

205 

216 

207 

206 

218 

78 

81 

78 

72 

71 

73 

77 

81 

96 

93 

98 

log 

112 

101 

112 

120 

86 
284 
231 
108 
210 

79 
"3 


TABLE  NO.  28 
The  Octave.    Rate  of  each  separate  tap.    Read  down. 


Rg 


93 

96 

91 

76 

95 

90 

94 

88 

95 

91 

93 

93 

8S 

99 

99 

102 

90 

90 

93 

89 

88 

88 

90 

92 

96 

99 

94 

88 

89 

85 

86 

91 

98 

92 

93 
90 


Average  rate  for  each  three-second  period.    Read  across. 


d' 


Rg 

Po, 
Rk 
Ho 
Fr. 

Ta. 
Pu 


93 

94 

93 

86 

go 

90 

g2 

93 

272 

261 

277 

246 

232 

262 

264 

256 

251 

250 

259 

256 

262 

260 

259 

268 

107 

108 

102 

97 

104 

106 

m 

198 

199 

192 

2^5 

216 

207 

205 

206 

81 

81 

81 

78 

87 

82 

80 

81 

130 

138 

116 

112 

114 

114 

124 

120 

93 

252 
266 
106 
212 
82 
147 


STUDIES  IN  MELODY.  77 

§33  In  the  last  two  tables  to  be  presented,  Nos.  29  and 
30,  are  shown  the  rates  of  tapping  during  the  hearing  of  a 
longer  group  of  tones.  Here  the  exact  number  of  tones  was 
not  told  in  advance,  the  observers  being  informed  merely 
that  they  might  expect  several  more  than  the  usual  number. 
The  two  "melodies"  are  alike  in  that  they  both  start  and 
end  with  "c,"  and  both  use  the  same  intermediate  tones;  but 
they  differ  in  the  order  of  these  tones.  The  first  group  moves 
slowly  but  naturally  forward,  and  at  length  comes  inevitably 
to  rest  on  the  last  of  the  seven  tones.  The  second 
moves  as  slowly  and  as  regularly,  and  reaches  the  same  goal, — 
and  yet  the  goal  is  not  the  same.  Subjectively  it  is  no  goal 
at  all.  None  of  the  observers  knew  when  it  had  been  reached 
until  the  tones  abruptly  ceased,  whereas  with  the  previous 
group,  all  but  one  reported  that  they  knew  the  last  tone  was 
the  last  as  soon  as  it  began  to  sound.  The  first  sequence, 
then,  is  a  genuine  melody;  the  second  is  not. 

One  or  two  typical  introspections  may  be  quoted  as  repre- 
sentative of  the  sort  of  experience  which  was  more  or  less 
common  to  all  of  the  observers.     Rk.  (first  seven-tone  group.) 

During  the  first  three  notes  I  did  not  know  what  was  the  melodic 
meaning  or  general  direction,  but  on  the  fourth  note  it  took  shape  and 
I  anticipated  what  the  next  would  be,  and  so  on  to  the  last.  The  last 
was  definitely  final.  It  didn't  occur  to  me  that  there  might  have  been 
more  tones  imtil  you  suggested  the  possibility  of  it. 

(Second  group.)  The  third  note  was  not  what  I  expected.  The 
sixth  would  possibly  have  made  a  good  ending.  The  last  note  was 
a  disappointment;  it  wasn't  offensive,  but  obviously  was  not  the  best 
possible. 

None  were  satisfied  with  the  ending  of  the  second  group 
of  tones;  all  thought  it  more  or  less  incoherent  throughout  and 
hard  to  grasp.  But  with  the  first  group  every  observer  with 
one  exception  was  sure,  when  the  last  tone  had  been  reached, 
that  that  was  to  be  the  final  tone.  The  one  exception,  Pu., 
could  not  give  a  definite  answer  to  the  question  whether  the 
ending  were  a  surprise  or  not,  whether  or  not  anything 
further  was  anticipated. 


78  W.  VAN  DYKE  BINGHAM. 

TABLE  NO.  29 
Group  of  tones  judged  to  be  a  melody.    Rate  of  each  separate  tap.    Read  down. 


c' 

e' 

S' 

e' 

/' 

d' 

c' 

252 

238 

236 

238 

252 

228 

221 

238 

258 

228 

250 

248 

246 

228 

23s 

240 

228 

220 

222 

222 

256 

204 

256 

236 

250 

237 

236 

237 

208 

220 

236 

240 

240 

222 

260 

256 

230 

236 

237 

246 

208 

233 

218 

238 

251 

186 

233 

246 

250 

238 

238 

220 

205 

211 

220 

222 

246 

219 

218 

256 

228 

236 

232 

221 

229 

220 

252 

261 

236 

254 

241 

254 

236 

250 

256 

220 

206 

233 

233 

228 

246 

212 

218 

236 

237 

246 

258 

211 

254 

220 

231 

257 

228 

234 

244 

236 

246 

237 

252 

20s 

237 

224 

237 

237 

245 

238 

256 

254 

227 

254 

257 

217 

220 

217 

220 

254 

256 

226 

242 

234 

245 

250 

252 

232 

212 

203 

220 

238 

238 

246 

240 

234 

236 

238 

2S7 

226 

210 

220 

222 

220 

236 

246 

236 

Po. 


236 

238 
254 
238 

220 

236 

236 

238 
238 
236 
236 
244 


Average  rate  for  each  three-second  period.    Read  across. 


f        d' 


Po. 

Rg 
Rk 
Ho 
Fr. 
Ta 
Pu 


241 

244 

247 

227 

221 

219 

22y 

241 

242 

227 

251 

244 

98 

98 

92 

95 

90 

89 

97 

91 

88 

93 

95 

96 

200 

190 

196 

195 

181 

180 

190 

191 

ig8 

207 

205 

208 

87 

80 

87 

80 

78 

83 

82 

82 

79 

88 

90 

92 

205 

229 

228 

222 

223 

216 

202 

206 

212 

212 

216 

206 

69 

70 

68 

67 

63 

74 

68 

66 

58 

67 

68 

66 

102 

98 

105 

97 

lOI 

no 

114 

107 

108 

102 

106 

109 

239 

94 
215 

88 
216 
69 
112 


TABLE  NO.  30 

Seven-tone  group  judged  not  to  be  a  melody.    Average  rate  by  three-second  periods. 
Read  across. 


c' 

f 

d' 

g' 

e' 

/' 

c' 

Po 

260 

254 

261 

266 

276 

263 

280 

238 

264 

247 

260 

253 

265 

Rg 

104 

108 

103 

log 

112 

112 

140 

114 

102 

lOI 

105 

108 

Rk 

152 

153 

162 

169 

172 

168 

168 

163 

169 

157 

152 

153 

171 

Ho 

102 

112 

HI 

100 

100 

102 

99 

lOI 

106 

772 

105 

110 

102 

Pu 

117 

105 

122 

117 

110 

122 

121 

113 

"5 

118 

118 

125 

122 

In  the  tables  the  changes  of  rate  are  shown  throughout  the 
course  of  the  melody,  but  the  ones  which  are  of  special 
significance  for  our  purposes  are  of  course  those  accompany- 
ing the  strongly  contrasted  feelings  at  the  end  of  the  tonal 
sequences.  At  the  close  of  the  first,  every  record  reveals  an 
acceleration  in  the  rate  of  tapping.     In  marked  contrast  are 


STUDIES  IN  MELODY. 


79 


the  retardations  found  at  the  close  of  the  other  sequence. 
(See  accompanying  graph,  Fig.  3.) 


Seven  tones  judged  to  be        ' 
a  melody. 


c"  e     %■    e      f    d 


Seven  tones  judged  to  be 
no  melody. 


f    d'  %■     e      f    c 


Figure  No.  3.  Effects  of  a  Melody  A^fD  a  Non-Melody  Contrasted. 
Each  tone  sounded  for  three  seconds.  Graphs  represent  rate  of  tapping  during  each 
of  these  three-second  periods.  Note  general  tendency  toward  increase  in  rate  at 
close  of  melody,  and  absence  of  such  acceleration  at  close  of  non-melodic  sequence. 

§34  It  remains  to  summarize  and  evaluate  the  foregoing 
experimental  data. 

The  facts  which  stand  out  with  most  prominence  are,  first 
the  correlation  between  the  beginning  of  a  tonal  sequence  and 
a  drop  in  rate  of  tapping;  second,  the  correlation,  nearly  as 
close,  between  the  conclusion  of  a  tonal  sequence  and  an 
increase  in  rate  in  case  the  observer  knows  in  advance  how 
-many  tones  are  to  be  expected ;  third,  the  retardation  of  rate 
at  the  end  of  a  two-tone  sequence  when  the  observer  has  been 
led  to  expect  three  tones,  the  sequence  being  one  which  under 
the  usual  conditions  produced  acceleration  instead  of  retarda- 
tion of  rate;  fourth,  retardations  at  the  close  are  much  more 
frequently  encountered  among  those  two-tone  intervals  which 


8o  W.  VAN  DYKE  BINGHAM. 

are  judged  to  be  "unrelated",  incoherent  or  decidedly  "incom- 
plete,' '  than  among  intervals  judged  to  be  melodious,  coherent 
or  characterized  by  finality;  {vid.,  especially,  descending  vs. 
ascending  fourth,  ascending  vs.  descending  fifth,  minor  sixth 
vs.  major  third) ;  fifth,  the  return  to  a  first  tone  is  felt  as  giv- 
ing unity  to  a  three-tone  group,  and  retardations  at  the 
close  are  not  often  met  with,  no  matter  how  unrelated  and 
foreign  the  middle  tone  may  have  been ;  sixth,  longer  sequences 
of  tones,  the  pitch  relations  of  whose  elements  give  to  them 
opposite  characters  as  regards  internal  coherence  and  final- 
ity, produce  opposite  effects  upon  the  rate  of  tapping. 

In  an  examination  of  our  data,  these  six  points  come  to 
view.  The  attempts  to  apply  our  hypothesis  in  detail  to 
some  of  the  results  must  be  considered,  however,  simply  as 
indications  toward  a  possible  development  of  the  method  into 
an  analytic  tool  of  much  usefulness,  rather  than  as  bring- 
ing forward  further  positive  evidence  on  the  question  of  the 
motor  aspects  of  the  perception  of  a  melody. 


PART   IV. 

SUGGESTIONS  TOWARD  A  MOTOR  THEORY  OF  MELODY. 

Such  evidence  of  the  interconnection  between  muscular 
activity  and  melody  experience  as  has  been  here  adduced  is 
too  slender  to  serve  as  the  support  of  an  elaborate  and  detailed 
theory.  But  the  broad  lines  along  which  a  motor  theory 
of  melody  must  some  day  be  worked  out  may  be  with  pro- 
priety suggested  here,  as  harmonizing  with  the  experimental 
facts  in  so  far  as  they  are  available. 

§35.  Every  melody,  like  every  other  experience  which  is 
a  'whole,'  must  have,  in  Aristotelian  phrase,  "a  beginning,  a 
middle  and  an  end."  A  motor  theory  of  melody  finds  the 
'beginning'  in  the  upsetting  of  established  muscular  tensions 
which  the  onset  of  the  tonal  sequence  involves. 

The  'middle'  includes  the  taking  of  the  proper  'attitude, ' 
the  organization  of  a  set  of  incipient  responses,  and  then  as 
the  tonal  sequence  proceeds,  the  making  of  these  responses 
explicit  and  overt  in  the  acts  of  responding  to  the  successive 
tones.  Each  tone  demands  a  specific  act  of  adjustment  for 
which  a  general  and  also  a  more  or  less  specific  preparation 
has  already  been  made,  and  each  contributes  in  turn  to  the 
further  more  definite  organization  of  the  total  attitude.  If 
a  tone  appears  which  is  of  such  a  pitch  that  an  entirely  new 
adjustment  is  necessary,  that  tone  is  unrelated:  unity  is 
destroyed;  the  succession  of  tones  is  not  a  melody.  But  if 
the  new  tone  is  so  related  to  its  predecessors  that  it  institutes 
a  response  which  is  in  part  a  continuation  of  the  act  already 
in  progress,  the  unity  is  preserved. 

The  'end'  comes  only  with  the  arrival  of  a  phase  of  the  com- 
plex ongoing  activities  in  which  the  balanced  tensions  can 
merge  into  each  other  and  harmoniously  resolve  their  oppos- 
ing strains.     This  becomes  possible  when  a  sufficiently  defi- 


82  W.  VAN  DYKE  BINGHAM. 

nite  set  of  expectations  has  been  aroused  and  then  satisfied. 
Here  we  find  a  reason  why  a  close  on  the  tonic  has  to  be 
'prepared  for,'  in  musical  phraseology,  by  a  'leading  tone' 
not  in  the  tonic  chord.  The  expectations,  the  muscular 
strains  and  tensions,  must  be  developed  to  a  certain  degree 
of  definiteness  of  organization  before  a  return  to  the  tonic 
can  serve  as  the  cue  for  a  general  'resolution.'  ^Losung' 
describes  the  close  of  the  motor  process  somewhat  better  than 
its  English  equivalent,  relaxation.  A  single  muscle  can 
relax.  But  this  process  of  muscular  Losung  which  marks  the 
end  of  a  melodic  phrase,  a  spoken  sentence,  or  a  rhythmical 
period,  is  more  than  mere  relaxation;  it  is  an  organized, 
balanced  muscular  "resolution,"  to  borrow  a  very  apt  tech- 
nical term  from  the  musicians. 

Of  some  such  'beginning'  and  of  some  such  'end,'  even  so 
crude  and  apparently  remote  a  line  of  experimental  attack 
as  the  one  we  have  used,  has  furnished  an  indication.  In 
order  to  learn  about  the  nature  of  the  'middle'  muscular  proc- 
esses a  more  refined  way  of  approach  to  the  delicately  com- 
plex mechanism  of  the  melody  experience  must  be  devised. 
One  would  like  best  of  all  to  record  the  tensions  of  the  laryn- 
geal muscles  when  no  sound  is  being  emitted.  Here  doubt- 
less is  one  of  the  centers,  with  many  persons  at  least,  of 
those  activities  by  means  of  which  a  series  of  separate  musical 
sounds  is  bound  together  into  the  unified  experience  we  call 
a  melody.  Already  some  few  significant  facts  have  been 
accumulated  regarding  vocal  tensions  during  auditory  stimu- 
lation. Seashore  and  Cameron  have  independently  demon- 
strated that  a  vocal  tone  sung  against  an  auditory  distrac- 
tion tends  to  vary  toward  a  pitch  which  is  consonant  with 
the  distracting  tone.^ 

Is  this  muscular  process  whose  arousal  and  subsidence  give 
shape  and  unity  to  a  melody,  a  rhythm?  It  certainly  has 
many  of  the  earmarks  of  a  rhythm, — its  motor  mechanism, 
its  relaxation  following  tension,  its  conscious  aspect  describ- 
able  as  a  satisfaction  of  expectation — all   these  would  lead 

1  E.  H.  Cameron.  "Tonal  Reactions."  Psych.  Reo.  Mono.  Supplements.  1907, 
8,  287. 


STUDIES  IN  MELODY.  83 

one  to  call  it  a  sort  of  macro-rhythm,  a  giant  process  similar 
in  its  essential  nature  to  a  rhythm  in  the  usual  sense.  But 
there  are  fundamental  objections  to  such  an  identification, 
chief  of  which  are  (i)  that  a  rhythm  involves  repeatedly 
recurrent  stresses,  with  recognition  of  similarities,  as  this 
'ground-sweir  muscular  process  does  not,  and  (2)  that  a 
certain  regularity,  with  possible  variations  between  well- 
defined  limits  only,  is  essential  to  rhythms.  The  two  phenom- 
ena, although  both  motor  at  basis,  must  not  be  confused. 

The  experimental  study  of  rhythm  has,  however,  disclosed 
a  motor  phenomenon  essentially  like  the  large,  basic  motor 
activity  underlying  a  melodic  unity.  I  refer  to  the  particular 
sort  of  muscular  tension-relaxation  process  which  Stetson^ 
found  to  be  essential  to  the  unity  of  a  group  of  rhythmic  ele- 
ments felt  to  constitute  a  verse,  or  a  rhythmic  phrase. 

Using  a  modification  of  the  principle  of  the  phonographic 
recorder,  Stetson  made  records  of  spoken  verse,  and  measured 
with  microscope  and  micrometer  the  duration  and  the  rela- 
tive intensity  of  the  separate  syllables. 

In  unrhymed  stanzas  the  duration  of  the  verse  pause  was 
found  to  vary  widely,  but  it  was  invariably  longer  than  the 
foot  pause.  The  typical  dynamic  shading  of  the  verse  was 
found  to  be  of  the  crescendo-  diminuendo  form.  The  intro- 
duction of  rhyme  often  shifted  the  climax  of  the  crescendo 
to  the  final  foot  by  increasing  the  intensity  of  the  rhymed 
syllable.  Although  as  great  a  verse  pause  was  found  to  be 
possible  with  rhyme  as  without  it,  the  presence  of  rhyme 
tended  to  shorten  the  verse  pause,  to  bring  the  verse  to  a  close 
more  rapidly. 

Within  the  verse  the  general  form  of  the  syllable  as  it  appears  in  the 
mass  of  closely  written  vibrations  often  varies,  but  nearly  always  shows 
a  square  end.  Several  very  common  shapes  are  noticed  and  appear  in 
the  record  as 'truncated  cones/ 'boxes' and 'truncated  spindles.'    .     . 

One  syllable  form  has  an  especial  interest,  because  of  its 

bearing  on  the  problem  of  'finality'  feeling  at  the  close  of  the  verse.    At 
the  close  of  each  verse,  whether  with  or  without  rhyme,  the  syllable 

iR.  H.  Stetson.  Rhythm  and  Rhyme.  Harvard  Psych.  Studies,  Vol.  1.  Psych. 
Rev.  Mono.  Suppl.     1902,  4,  413. 


84  W.  VAN  DYKE  BINGHAM. 

form  is  always  a  'cone.'    Of  about  600  verses  measured  not  more  than 

15  are  exceptions  to  this  rule 

The  form  very  rarely  occurs  within  the  verse,  and  when  it  does  it  is 
usually  before  some  caesura,  or  under  unusual  conditions. 

This  '  cone'  form  of  the  closing  syllable  of  the  verse  indicates  a  fall- 
ing of  the  intensity  of  the  voice.  It  is  often,  though  not  always,  asso- 
ciated with  a  fall  in  the  pitch,  showing  relaxation  of  the  vocal  cords. 
It  seems  to  be  an  indication  of  the  dying  out  of  the  intensity  factor,  a 
sinking  of  the  tension,  at  the  close  of  the  verse.  In  the  case  of  unrhymed 
verses,  with  long  verse  pause,  the  cone  is  often  very  much  elongated,  and 
it  is  quite  impossible  to  say  where  the  sound  ceases.' 

It  will  not  be  necessary  to  treat  here  of  those  portions  of  the 
motor  theory  of  rhythm  which  explain,  as  the  central,  or 
"mental  activity"  theories  have  failed  to  do,  the  peculiar 
nature  of  the  various  sorts  of  unit  groups.^  We  shall  briefly 
sketch  only  so  much  of  the  theory  as  is  requisite  to  explain 
the  larger  groupings  such  as  the  phrase,  the  verse,  the  period. 

Stetson's  theory  of  rhythm  assumes  a  movement  cycle  in- 
volving the  activity  of  two  opposing  sets  of  muscles.  The 
varying  tension  between  these  muscle  sets  as  beat  follows 
beat  never  entirely  disappears  until  the  close  is  reached. 

The  continuity  of  the  rhythmic  series,  whereby  all  the  beats  of  a 
period  seem  to  belong  to  a  single  whole,  is  due  to  the  continuity  of  the 
muscle  sensations  involved  and  the  continuous  feehng  of  slight  tension 
between  the  positive  and  negative  muscle  sets;  nowhere  within  the  period 
does  the  feeling  of  strain  die  out. 

But  at  the  close  of  the  period  we  have  a  pause  which  is  demon- 
strably not  a  function  of  any  of  the  intervals  of  the  period.  During  this 
pause  the  tension  between  the  two  sets  '  dies  out, '  and  we  have  a  feeling 
of  finaUty.  This  gradual  dying  out  of  the  tension  is  clearly  seen  in  the 
constant  appearance  of  the  cone-shaped  final  syllable  at  the  end  of  each 
nonsense  verse. 

The  period  composed  of  a  number  of  unit  groups  (the  verse,  in  non- 
sense syllables)  has  a  general  form  which  suggests  strongly  that  it  has 

1  L.  c,  447. 

^  For  a  determination  and  explanation  of  these  peculiarities,  such  as  the  closer 
proximity  of  the  unaccented  to  the  accented  beat  in  the  iambic  as  contrasted  with  the 
trochaic  foot,  etc.,  cf.,  Stetson,  "A  Motor  Theory  of  Rhythm  and  Discrete  Succession," 
Psych.  Rev.  1905, 12,  293  ff. 


STUDIES  IN  MELODY.  85 

the  unity  of  a  single  coordinated  movement.  There  is  no  more  reason 
for  assuming  a  transcendental  mental  activity  in  the  case  of  a  rhythmic 
period  than  in  the  case  of  a  single  act  which  appears  in  consciousness  as 
a  unity At  some  point  in  the  pe- 
riod there  is  a  definite  climax,  a  chief  accent;  the  movement  'rises'  to 
that  point  and  then  falls  off.  This  is  strikingly  seen  in  nonsense  verses 
spoken  with  a  heavy  accent  within  the  verse.  The  accent  does  not 
stand  out  from  a  dead  level,  but  the  verse  culminates  at  that  point.* 

As  a  result  of  his  previous  study  of  perceived  as  opposed 
to  produced  rhythms  and  especially  the  effects  of  rhyme  and 
of  wide  variations  of  tempo, — '  lags, ' — introduced  into  differ- 
ent portions  of  the  verse  and  of  the  stanza.  Stetson  was  led  to 
the  conclusion  that 

there  is  some  definite  process  at  the  end  of  the  verse  which  marks 
the  close  of  the  verse  and  which  takes  more  time  in  the  case  of  blank  verse 
than  in  the  case  of  rhymed  verse.  If  we  conceive  the  end  of  the  verse  as 
a  point  where  a  dying  out  of  the  tension  occurs,  we  may  imagine  that 
the  rhyme  brings  an  emphasis,  and  becomes  a  quahtative  signal  for 
this  release.  The  slight  increase  of  intensity  on  the  rhyme  contributes 
to  the  breaking  up  of  the  coordination,  and  at  the  same  time  exhausts 

and  satisfies  the  feeUng  of  tension  which  the  verse  embodies 

A  quahtative  change  may  be  supposed  to  produce  the  effect  more  rapidly 
than  the  simple  dying  out  of  the  tensions,  which  occurs  in  blank  verse 
without  a  differentiated  end  accent.^ 

This  finality  effect  which  rhyme  augments  is  entirely  analo- 
gous with  the  finality  phenomenon  in  melody.  We  have  seen 
that  in  three-tone  sequences  mere  return  to  the  original  pitch 
may  furnish  the  qualitative  signal  for  the  muscular '  resolution. ' 
If  the  final  tone  is  not  merely  a  repetition  of  the  initial 
tone,  but  has  also  the  characteristics  of  a  '  tonic, '  the  com- 
pletion of  the  finality  process  is  much  more  definitely  assured. 
A  third  cause  which  sometimes  operates  to  produce  the 
same  effect  is  the  mere  satisfaction  of  expectation.  If  one 
hears  a  certain  irregular  series  of  pitches,  "related"  or  "unre- 
lated," often  enough  so  that  the  final  tone  can  be  recognized 
as  such,  one  comes  to  feel  that  the  group  has  a  certain  sort  of 


1  Rhythm  and  Rhyme,  4SS- 


86  W.  VAN  DYKE  BINGHAM. 

unity  even  though  there  is  neither  a  return  to  a  starting  point 
nor  an  end  on  the  tonic.  The  same  holds  true,  to  a  certain 
extent,  with  reference  to  an  unfamihar  succession  of  tones 
whose  number  is  Icnown  in  advance.  If  the  observer  is  told 
to  expect  four  tones,  a  motor  disposition  or  attitude  is  estab- 
lished which  constitutes  a  preparedness  to  react  to  four  tones, 
and  if  only  three  tones  are  heard,  the  finality  effect  may  fail 
to  appear,  although  the  third  and  final  tone  is  at  once  a 
tonic  and  a  return  to  the  pitch  of  the  initial  tone  of  the 
sequence. 

In  each  of  these  types  of  melodic  finality,  the  closing  tone 
institutes  a  response  which  is  not  wholly  a  new  reaction  but 
which  is,  on  the  contrary,  the  completion  of  an  act  already  in 
progress.  The  feeling  of  finality  arises  only  when  the  comple- 
tion of  the  act  issues  in  a  muscular  relaxation  which  is  a  dying 
out  of  balanced  tensions.  The  facts  regarding  those  finality 
effects  which  are  due  to  the  falling  inflection  also  coincide  with 
such  a  view.  Rise  in  pitch  is  not  merely  a  result  of  increased 
tension  of  the  vocal  apparatus :  it  likewise  produces  increased 
muscular  tension  in  the  hearer.  A  falling  inflection  at  the 
close  consequently  serves  to  hasten  the  relaxation  process 
which  marks  the  completion  of  the  melody. 

Finally,  a  motor  theory  of  melody  makes  possible  an  unam- 
biguous statement  of  the  nature  of  melodic  "relationship." 
Two  or  more  tones  are  felt  to  be  "related "  when  there  is  com- 
munity of  organized  response.  "Unrelated"  pitches  fall 
apart  because  each  demands  its  own  separate  attentive  act  of 
adjustment;  but  with  "related"  tones  the  attitude  which 
appears  as  a  response  to  the  first  is  a  preparation  for  the 
response  to  the  second  and  is  completed,  not  destroyed,  by 
that  response.  The  feeling  of  "relationship"  is  the  feeling 
that  arises  when  the  tones  elicit  reactions  which  are  in  some 
measure  common.  When,  on  the  other  hand,  the  first  tone 
calls  up  one  set  of  associates  and  establishes  a  certain  attitude 
or  organization  of  incipient  tendencies,  while  the  second  tone 
tends  to  call  up  a  set  of  associates  and  establish  an  attitude 
which  is  at  variance  with  the  first,  there  can  be  no  adequacy  of 
coordinated  response  and  the  feeling  of  "relationship"  is  pre- 
vented from  arising. 


STUDIES  IN  MELODY.  87 

The  origin  of  these  well-articulated  responses  which  gener- 
ate the  feelings  of  "relationship"  is  not  to  be  sought  in  a 
single  source.  The  operation  of  two  main  forces  must  be 
distinguished — one  of  them  sensory,  the  other  associative. 
The  first  of  these,  the  phenomenon  of  consonance,  is  native 
and  doubtless  has  its  basis  in  the  relatively  simple  action  of 
the  sensory  apparatus  in  responding  to  auditory  stimuli  which 
are  more  or  less  similar — are,  indeed,  in  a  measure  identical. 
But  although  the  basis  for  consonance  inheres  in  the  inborn 
structure  of  the  nervous  system  and  the  acoustical  properties 
of  vibrating  bodies,  nevertheless  it  is  a  commonplace  of  musi- 
cal history  and  observation  that  these  same  native  tendencies 
are  subject  to  tremendous  modification  in  the  course  of  experi- 
ence. One  race,  one  age  hears  as  consonant  intervals  which 
another  age  or  race  has  never  learned  to  tolerate;  and  within 
the  history  of  individuals  it  is  easily  observable  that  conso- 
nance and  dissonance  are  merely  relative  terms  whose  deno- 
tation shifts  with  growing  experience.  Moreover  the  whole 
complex  group  of  phenomena  we  call  tonality  bears  witness 
to  the  power  of  association  to  amplify  and  organize  these 
native  feelings. 

But  the  associative  factor  or  the  factor  of  experience  is 
directly  efficient  in  determining  what  tones  shall  be  felt 
as  "related,"  quite  apart  from  any  effects  which  it  has  upon 
judgments  of  consonance.  Mere  custom,  mere  habituation 
to  a  certain  succession  of  pitches  results  in  a  facility  of  recog- 
nition and  response  which  is  capable  of  generating  these 
feelings  of  "relationship."  The  same  kind  of  coordinated 
reaction  is  instituted  and  this  makes  possible  the  same  result- 
ant feeling  as  that  brought  about  by  response  to  two  succes- 
sive consonant  tones.  The  ' '  relationship  "  is  in  both  instances 
traceable  to  the  motor  phase  of  the  process. 

The  unity,  then,  which  marks  the  difference  between  a  mere 
succession  of  discrete  tonal  stimuli  and  a  melody,  arises  not 
from  the  tones  themselves:  it  is  contributed  by  act  of  the 
listener.  When  tone  follows  tone  in  such  a  manner  that  the 
hearer  can  react  adequately  to  each,  when  the  response  to 
the  successive  members  of  the  series  is  not  a  series  of  separate 


88  W.  VAN  DYKE  BINGHAM. 

or  conflicting  acts  but  rather  in  each  instance  only  a  continu- 
ation or  further  elaboration  of  an  act  already  going  forward, 
then  the  tones  are  not  felt  as  discrete,  separate,  independent, 
but  as  "related"  to  each  other.  And  when,  finally,  the  series, 
of  tones  comes  to  such  a  close  that  what  has  been  ^coiltinuous 
act  of  response  is  also  brought  to  definite  compfeyon,  the 
balanced  muscular  "resolution"  gives  rise  to  the  feeling  of 
finality,  and  the  series  is  recognized  as  a  unity,  a  whole,  a 
melody. 


14  DAY  USE 

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